In general, most economies do not save or invest enough. This would increase savings and investment. It would generally be a good thing.
You could certainly prevent this with a wealth tax. The return after inflation on the stock market is currently around 7% in the United States (for a time period long enough to include the whole economic cycle). So a 7% tax would eat up all the returns. Nothing left for maintenance of the cryogenic facility. People would go broke while frozen and wake up poor.
Even without explicit government action, the possibility exists that an increase in savers would push market returns down. There is some speculation that the recent bubble markets in internet stocks and housing were partially a result of too much passive savings. If that's true, then the very increase in savings would cause it to become less profitable.
There is a difference between passive investments, like stock index funds, and active investments. People who actively manage their investments will get better returns under this kind of plan. Active investments include starting a business, managing real estate, and engaging in microloans. None of these activities are possible while frozen. In theory, you could hire someone to do this for you, but the labor shortage of everyone freezing would tend to make hiring prohibitively expensive.
For the sake of argument, assume that at the start, low wages are \$10 per hour and the median wage is about \$30 an hour. It costs \$1000 for the cryopod and \$100 a year for maintenance (these prices seem low but are consistent with the cost of a refrigerator). Assuming a real interest rate of .5%, that's a \$21,000 initial investment. And that's just to break even. To get rich, you would need more than that. Let's figure on \$30,000.
If the living wage is about \$15 an hour, then if you work at \$30 an hour and put \$10 an hour into savings, it will take 3000 hours to put away enough to sleep. That's about a year and a half of work, figuring 250 eight-hour work days a year (261 weekdays in the average year; 11 holiday/vacation days). And of course you won't necessarily enter the workforce at \$30 an hour. You either need a successful education or work history to make the median wage. Figure five years for the education or twenty years for the work history.
Anyway, assume you have your \$30,000 stake. \$21,000 immediately goes to the cryo. That leaves you with \$9000. Putting it in the stock market and waiting will double your money after inflation around every ten years. So after a century frozen, you will have \$9 million (which may be \$144 million in nominal terms; inflation will have doubled four times). But normal taxes in the current US would be 20.9% on long term investments for high income people. So you're down to \$7 million.
Now, what happens if the government changes taxes? For example, if taxes were increased to 70% with no special investment rate and payroll taxes were extended to investments with no cap. That would produce a tax rate of 85.3% in the US. The \$9 million would drop to \$1.3 million. Set aside \$200,000 for living on for five years and invest the rest. That's probably enough for a stable \$40,000 a year income. Of course, when you were frozen, you were making \$60,000 a year.
All this ignores other possible problems. In Japan, the stock market stagnated for more than a decade. Twenty years of that at the wrong time would drop the return to \$300,000. That's a \$10,000 a year income where \$30,000 is a living income.
Remember the speculation that more savings would reduce stock market returns? If we reduce stock market returns from 7% to 3.5%, it would take twice as long for our investment to double. So a single century would only produce about \$290,000.
The other side of that is that labor would increase. So that \$30 an hour job might become a \$60 an hour job. So someone who did not freeze might make \$120,000 a year while the frozen could hope for \$40,000 a year. Although, people would probably stop doing it before things got to that point.
Realize that the benefits of not paying Social Security for a century are huge. A pro-cryo government might be able to completely fund its borrowing just with that money.
Remember that one of the problems is that the tax rate might increase while you were sleeping. An obvious response to that is a government where the tax rate cannot increase. Consider the possibility of a space station establishing itself as a nation state. It has plenty of electricity to maintain cryo chambers. It could pay a good wage to people who would maintain its systems and might offer a cryo citizenship. Taxes would be fixed in the constitution and flat across people who are and are not frozen.
We've been talking about this as if it were a perfect program. But the reality is that no technology is 100% reliable. Even a .001% failure rate a year adds up over time. What happens to someone who can't be unfrozen? If not noticed until the decant time arrives, their heirs are either frozen themselves or dead of old age.
Another issue is that people who are frozen aren't raising kids. But it's not hard to see the process costing enough to use up the child-bearing years in making enough of a stake to afford it.
The alternate possibility is that people will have kids and get caught up in their families rather than freezing themselves. When are parents willing to step away from their children? When the children have children of their own? When those grandchildren go off to college?
This is essentially a program for loners. Most people are not loners. Most people have friends and family that they won't abandon for an uncertain future. While there may be a logical argument in favor of it, it is not an argument that works emotionally for someone who feels part of a larger group.
I'm not saying that no one will participate. I'm saying that only a small number of people will participate. A few well-to-do people who have outlived their close families. The occasional small lottery winner. Small groups of people who feel disconnected from everyone else. A celebrity hoping to make a comeback while still young and good looking. A spurned lover.
If only a few people participate, there are unlikely to be serious economic consequences.