There are still many dangers to consider which make things difficult.
In the current scenario you have quasi-indestructible bodies, but everything else is made of normal matter.
Space Hazards and (Ship-)Infrastructure
Imagine the spaceship getting destroyed or otherwise wrecked in deep space (especially: communications, energy, propulsion, rescue shuttles). The bodies would be doomed to an eternal life in the endlessness of space. That could drive them crazy or trigger other things. If the power source is cut, you will need to know what happens to them if the chambers cannot provide recharging anymore (some kind of collective deep-sleep, mutiny/insurgence, fight for the remaining working chambers, and the like).
The bodies are also of finite size still, thus the spaceships need to be sized accordingly. All the challenges that come with this would not be alleviated. You need a dock where to build it, material, time, knowledge, man-power, etc. Technical failures occurring later would also not be excluded and they need maintenance.
Thus, making certain roles in the crew necessary for example engineers, while other roles can be dropped like chefs, doctors, etc (see below). Those still need universities and everything to get their knowledge from somewhere (on a home planet probably).
The things you would save are for example: Life support, maybe beds (and their space) because you could provide a large dorm room with those chambers (no need for privacy?), all the cargo space for foodstuff, kitchen areas, and medical/infirmaries, probably also bathrooms/toilets and other sanitation/waste. You probably still need entertainment, social and private areas for them and storage space for personal items, and important non-food items, like spare parts for the maintenance.
The space ships would have a very different layout than ours, because of the mentioned "superfluous spaces" that can be used otherwise. For example adding many sleeping chambers for large colony ships or something.
Prototype Scenario
The scenario reminds me of the Borg of StarTrek, concerning strengths and weaknesses (not appearance). I also like Trish's comparison to WH40k, very fitting extremes.
Power Source
There is one point to consider with the sleeping chambers and interstellar travel:
The ship needs a sufficiently capable power source which does not rely on sunlight alone. Or alternatively, you need a solution how to store a really large amount of energy (like large capacity batteries that were charged by solar energy). The reason is energy/light emitted from stars falls off rapidly with distance. It is already very faint just inside our solar system at the outer areas.
For example: Our Voyager1+2 which are the farthest away ("interstellar") objects in space we have contact to, do not rely on solar panels. They have a radio active power source to generate electricity.
I am not that familiar with the exact functionality, but I assume it goes something like this: There is a radio active source, emitting electrons, these are collected somehow and stored in a capacitor ("battery") until a sufficiently large charge has built up, then this is released into the circuitry gradually. If the battery is depleted, there is some time needed until it is charged again. Thus, you have a quasi-unlimited source (well, limited by the decay of the radio active material) for electrons but only available for certain phases with high amounts of pauses in between (which are timed in a way, that it is sufficient to send telemetry back to earth in regular time windows). "Always on" instruments need to have fitting "low energy profiles" to be powered by the (or a second) battery all the time.
Deadly Hazards
If they are vulnerable by "ripping apart" or "melting into plasma" or "being captured in a gravity well", there are other possibilities to "attack" them, which you would need to consider how this affects them. For example:
- Cryogens "Freezing" attacks
- Putting them into a particle accelerator
- Confine/capture them deprived of recharging facilities
- Attacks on their power supply infrastructure instead of their immortal bodies
- Making a ship disabled and adrift (covert-ops, open attacks) and put it into a direct course into the nearest sun
- Fancy anti-matter annihilations
- Or just a software bug that prevents waking everybody up.
Conclusion
As LazyLizard covered in the answer: Immortal bodies would enlarge the possible travelling distances a lot (still taking long times). But their lives would not be "problem-free" and also not that "harm-free" - it shifts the attack vectors to something different. Mainly because of the infrastructure they still are dependent on. But maybe they are just peaceful traders instead of murderous conquerors.