Short answer, no. The guns only require a hose hookup and are incompatible with any sort of pressure washer.
The cannons (which is what Superbee has and what you're probably thinking about) are around 150 bucks, and hook up to a pressure washer. Unfortunately, they require a quick-disconnect style hookup, and hooking them up to a sub-$200 pressure washer requires a hard to find adapter (any sort of pressure washer that's made of plastic uses what's called a Karcher-style or bayonet-style hookup).
Those cheapie pressure washers are not bad to have (I have a plastic 1600psi that I use for rims, wheel wells, and my undercarriage), but if you want the big foam cannon setup, it's going to cost you at least 450 to put it together.
My advice would be to spend the money on a Gilmour gun instead - they're 50 bucks, hook up to a hose, and work like a charm. I use one religiously and have not been able to justify the extra money for a foam cannon (yeah the thicker foam looks nice, but I get almost zero marring as it is) .