So a DDNS service works by having a "client" that updates the service with its IP should it ever change. A lot of routers these days have various DDNS clients built in as that makes sense (Here's mine):
So if you're asking does the SH3 have a DDNS client built in? Then the answer is no.
However, there are lots of clients, most of those services will have a client you can download to a PC or server that will do exactly the same thing. I have no idea how your HAM works, but if it's software running on a PC, that PC can run a DDNS client - and Virgin (or the SH3) won't stop that from working.
However, as Maximus says, the easiest and best thing to do is buy yourself a dedicated router and use that. You'll save yourself a lot of headache in the end.