I guess you would not have suggested it, RacerX, if it were not possible, but are most companies pretty agreeable to stuff like this?
I can't speak for "most" companies, as I have only driven for one. I can say however, that commons sense would dictate what can and cannot be done. Simply asking for something is always a great place to start. You don't ask, you don't get.
I have heard that some companies expressly forbid inverters, driver installed or company installed. Most likely because the folks running the show have had a few burned down trucks and are gun shy.
I have also heard that some companies will set rigs up just about any way a driver asks them to, and some companies don't really care.
I am fortunate to drive for a company that takes good care of their drivers (we are just another asset), and they purchase the high end trucks. The rigs are well appointed, premium upholstery, stereo, air conditioning front and rear, condo sleepers with inverters, refrigerators, and APU's.
Small companies can have their advantages.
When I was looking for a job driving trucks the big companies wouldn't even return my call or respond to my application for employment. Their loss.