Nooo! I hope you can avoid the PA if possible. It can be done, but if it's not done well it destroys much of what makes classical music so interesting and involving and different from many other forms of modern music, at least for me. It's much trickier to do well than reinforcing a rock band and sound guys who work bars around VCU that mostly play amplified stuff are not likely to master it quickly, and even if done technically well, changes important aspects of what makes 'chamber music' unique.
Hopefully they can simply select and play lively fortississimo pieces in decently live rooms without massive levels of background noise from HVAC/blowers, and if possible arrange things so people interested in the music can sit closer, and others can talk at the bar farther away.
Maybe reinforcement will be necessary, but I'd consider it a last resort. Treating it something like a traditional blugrass act playing around a couple mics in the middle of the group would probably be the most fruitful approach and less foreign to decent sound guys around there I'd think.
As for chamber groups playing amplified with close mic’ing, I've seen Turtle Island Quartet recently and Kronos Quartet a few times in the past, both of which were excellent sounding exceptions, and their playing styles and techniques take specific advantage of what the PA can do other than simply make them louder without timbre and dynamics suffering much for it. I was very interested to check out their reinforcement techniques and efforts. They played PA amplified in theaters, but obviously have made a long-term effort to perfect the reinforcement and are top of the crop.
But those groups have a different focus in that they are modifying the traditional definition of what chamber music has been and has sounded like. Since the goal here is instead performance of high-quality chamber music in non-traditional settings, (presumably traditional chamber music), it seems to me that preserving the traditional aspects of 'high-quality chamber music' which have value in those non-traditional settings is an important goal, as much as that’s possible.