It's a nice idea, but I foresee problems in the application.
When you create a vacuum around water, the water will evaporate and expand into a gas, raising the pressure until there is no longer a sufficient vacuum to support the evaporative state.
So you would need a vacuum pump that is sufficient enough to overcome this, and even more so do to the large volume chamber necessary to house the suit.
So not only would you need a fairly sizeable vacuum chamber which would be expensive, but you would also require a fairly powerful vacuum pump bordering on the industrial level, again, expensive.
Otherwise a more obtainable pump (like those used for vacuuming a/c systems) might do what you need, though I imagin it could take about 20~30 hours (I'm basing that on typical pumps used to service automotive a/c systems), at which point air drying might be faster.
Now assuming we can have an infinitely powerful vacuum pump to where the "if we can" issues don't exist, there's another problem.
As we remove the fastest of particles through evaporation (also removing the heat/energy), we leave the slowest of particles.
Assuming the pump is strong/fast enough to remove the gas and water vapor continuously, some of the water can actually start to freeze if the humidity is kept low enough.
Mind that conditions need to be just right for this simultaneous freezing/boiling state to occur (low pressure/humidity/temperature), but between forming tiny ice crystal (think of them as molecular razor blades), and the process of vacuuming out most/all of the moisture in the fabric, I would assume this would create a dry rotting effect for the material.
I can't be absolutely certain that the material would be damaged without actually performing such an experiment, but I do believe that exposing material/fabric/etc. to such extreme environments would not be good for its longevity.