Is this possible to a single extension on the IPPBX?

Before anyone jumps up and down, this is a standard feature of SIP and ANY SIP server should support this. It does NOT introduce any confusion as to where calls are connected etc. Any correct SIP implementation can do this without problem. So...

Can the Vigor IPPBX handle multiple simultaneous registrations to an extension?

I've only been using my IPPBX for a day or so and am new to the whole SIP technology. But if I'm understanding your question correctly, then yes, the IPPBX can handle up to six SIP registrations and point each to a handset, huntgroup or the auto attendant. As well as that, the Vigor350 phone can have up to 10 SIP accounts, so you can bypass the IPPBX and put the registration straight on the handset.

OK, that sounds good. But having a handset bypass the IPPBX is something to be avoided if possible as you then miss out on the PBX features.