If you can't join other peoples' teams with a BBA, you're quite possibly not going to be able to with DreamPi either, unless you have some sort of hardware issue -- be it a bad BBA (unlikely, since you can host teams), a bad network cable (also unlikely, since you can host teams), or some sort of misbehaving router.
For PSO (and any other games that support both the BBA and the modem), the BBA will almost certainly give you a better experience online with less random issues than you will have with a DreamPi (or any other modem-based solution). The exception would be if you have some sort of issue with network equipment on your end (like a misbehaving router) -- sometimes having a modern network stack forwarding on your requests can solve that particular issue, but it really is an issue with your networking hardware.
Also, just to dispel some old rumors and whatnot, the MTU shouldn't have any impact on PSO unless you have it set below a certain threshold (the suggested value of 1400 is fine here) or you have it set to something obviously too large or something else odd like that. By default, most routers will set your network MTU to somewhere around 1500, which will work just fine with PSO. The MTU is a maximum value for a single packet, and most of the time you won't be sending maximal length packets. Whatever your router normally has set as the default will probably work just fine.
Also, back to the original topic of the thread... I suspect that if you have the PSO Patcher right before PSO on your GDEMU SD card, you might be able to make it work. That said, you'd probably need a button soldered to your GDEMU to swap the virtual discs, which is probably more trouble than it is worth to most people.