A quick google suggests you can – but you still have to insert the full win7 version cd and run set-up:
Upgrade from trial to full
Scroll down to the section 'How do I get the upgrade key to activate?' and read through that section. I'd give that a try and see if it works.
Last week tried upgrading from outlook 2007 trial (downloaded) to full version (bought on CD) and it wouldn't accept the valid full version key, so I had to do a fresh re-install of Outlook. Then the PC had a conflict as it hadn't morphed the trial version into the full version (despite setting default clients), so I had to uninstall the trial version. But maybe it's different with a full O/S…
Edit: in response to thread answer above, see also this but I think it relates to the situation where you've bought one flavour of win7 which is different to the trial flavour.