I think the ADSL filters are mainly to isolate your voice calls from your BB. If you remove the filter you may get noises on your voice calls but I would expect the BB to work.
All telephone lines have a maximum number of pieces of equipment you can use. It's called the REN (Ring Equivalent Number). If you've exceeded this then you may get problems. Each piece of equipment should tell you on it's lable what the REN is and just add then together. I don't know if ADSL filters have a REN value. I'm sure someone elses will! Add them all up and ask Bt if you've exceeded the REN for your circuit.