This actually depends of the type and brand of the modem, I had a US robotics Courier V.Everything, which is the best dial up modem they make, and nothing could stop me from getting 53.3
With the older Software modems, picking up the phone may not disconnect you, but it usually makes you stop sending and recieving, and generally doesnt get fixed till you disco and reconnect.
Not much you can do about it though, cept get a good USR hardware modem.