Hi, Bithawk, and welcome to the forums.
No, the apps do not time out, however, without some sort of connection and a Google account to log into you will not be able to access the Play Store to update them.
however, if you have a WiFi connection, you can still update them but only when on WiFi.
I cannot get my Droid2 to the internet via Wi-Fi. I just did a factory reset. Logged back into my Wi-Fi, still no access to the internet.