Since TiBackup must have root to work (I'm guessing that is what was used to freeze apps since it is the most common app) yes, you will have to be rooted to "defrost" apps.
While rooting itself did not prevent the OTA updates from working, some root apps (like bionic bootstrap or safestrap) do make changes to the phone system that will prevent OTA updates from working.
IMHO, the easiest thing would be to just flash ICS with RSDLite.
Check out the first post here:
http://androidforums.com/bionic-all-things-root/480176-how-flash-5-9-905-gb-6-7-246-ics-rsdlite.html
(Thanks yet again
OutOfPhase)
Use the
6.7.246 FXZ ICS file. You could use the modified ICS file, that would let you keep your data but... It is HIGHLY recommended that you do a factory data reset after moving from GB to ICS to avoid problems. That basically means you are starting with a fresh clean phone on ICS.
The
6.7.246 FXZ ICS file erases all data from the phone in the process so you will save yourself a step and will end up with a fresh clean phone on ICS.
After installing ICS you can then decide if you want to root and go form there.
One other thing to note...
Once you flash the ICS update (either through RSDLite or OTA) there is no going back to GB. Period.
It is worth jumping to ICS but just be aware, there is no way to undo it once it's done.