With convenient energy source, like a thermonuclear reactor, yes, viable, no problems.
It does not have to be on coasts, in that case, we build 1000's km long oil transfer pipes, water is even easier.
U may also build some kind Acropolis, which is more or less closed loop with water, so it may have no need to replenish the water too much.
With renewable sources, everything isn't so well.
This or another way all energy comes from the Sun.
The cheapest and most renewable source of energy are the plants themselves. Everything you need is a plant seed, and care about it, and it will convert energy to food. After you give good care to it, and after some time passing by, you can eat the product, or feed it to livestock.
The point is, any energy which you will extract from renewable sources your intention is to feed this energy to the plants, and they are the bottleneck.
Photosynthetic efficiency - efficiency is about 1-2%
Some kind of delicious Nutrient paste may help, some kinda another way to generate food may greatly improve the efficiency of energy to food conversion.
With plants it needs about 10kW 24/7/365 - to feed one human.
Interesting maps of solar irradiation here - it varies 2500kWh/year/m2 for hot climate to 1500-700 kWh/year/m2 for mild and cold climate.
In average you need something between 350 to 800 square meters to feed a human (a bit more sophisticated system than usual green house, but theoretically)
For 100 billion people we need about 14-31% of surface of our Planet.
So answer is yes, no problem here.
If we think, the ocean is such sophisticated green house I mention before, it keeps the temperature in a lot of places above freezing, it stores energy, etc.
If we would like to improve the situation further, then the main problem which has to be attacked is the efficiency of plants itself.
New Way of Transforming CO2 Is More Efficient Than What Plants Do
By tinkering with the process that plants use to breathe in carbon dioxide, a team of German scientists has just discovered a far more efficient way to get rid of it. ..... Plants, algae, and other organisms turn CO2 into fuel. Erb and his colleagues reengineered this process, making it about 25 percent more energy efficient and potentially up to two or three times faster.
Based on Photosynthetic efficiency wiki article, maybe another 2-3 times improvement (convert not used light to useful one, make night period of breathing shorter)
Against solar panes etc as main source for all energy we may need(especially for food production), is the fact - animals, insects etc can't be a part of ecosystem of solar panes and wind turbines. But they can and are part of plants ecosystem - so if we have intention to keep Earth biosphere(and that is very important, as it is living history, living data base of genes which we may use for us in the future and which helps to understand evolution processes etc) - then we should have solutions which integrate earth biosphere. But keeping this biological base is expensive process by itself - but my recommendation is to keep it by any means possible - it will help us a lot in future and it is extremely expensive (energy wise) to generate it from scratch - maybe 10000 years using sun with 100% efficiency - at least in the way I can imagine for my self, but it is simplest and not very sophisticated one - just by keeping earth copies space habitats)
100 billion people is not a problem if we go to space, 100 billion and much more, and it is an easier way to solve the problem. Mention that just in case if you would like to consider such way to solve the problem.
Yes, it is possible to feed 100 billion people on the Earth, energy wise there is no problems, some technological challenges but no major problems.
And thanks to Bert Haddad for pointing out errors in calculation.