I dont' know what a BPP is, but for a NST you're hooked up to monitors around your stomach (and have to sit in one place) for 10-30 minutes until they get a good reading on the baby. Would your 3 yo be able to sit still that long and be entertained with a book or something? I don't know about FFX, but at VHC they do the NST in pretty small rooms so there's not much room to spread out and play.
When I did my NSTs at FFX in 2010, they did them in a large room with three curtained off areas so up to three women can be getting NSTs at a time. If your 3-year old won't wander and/or you can give him something to occupy him, you might be able to do it. However, you wouldn't want him wandering around into the other curtained areas. I saw some moms bring little DVD players and headphones for their kids to occupy them. I never had to have a BPP, but I assume that if this is needed, they'd bring you into one of the closed off ultrasound rooms.
Re: BPP and NST at Inova Fairfax