The program will finish the scan with the 'old' virus database and then will finish the update.
Well, they will correct me if the 'last' part of the scanning will be carried on with the 'new' one, I'm not sure.
What I'm sure is that won't be a moment that you'll be unprotected
Even with program updates, that requires booting, the new program only will be used on next boot, keeping the computer protected, at least, with the 'old' version until boot.