As Matisse and Andreas say, automatic transfer is, in principle, possible. But for various reasons (either on the aircraft side or the ATC client side) it does not always work.
However, I gather that in real life automatic transfers are far from seamless or 100% reliable either -- from speaking to friends who fly around Europe in CPDLC-equipped aircraft on a daily basis, I hear that quite often the automatic transfer fails and a manual login is required, logon attempts quite regularly fail (in some FIRs more than others!), etc etc... so this is not necessarily entirely a VATSIM issue!