Yes, let it run when you open it after the update. Afterwards, it should open fine. You may find that a few apps have to update on first run with the OS upgrade. Once it is all done, you will be pleased.
Sorry I can't help you more. My wife was like others until I pushed for her to delete old messages or use GV, which defaults to 30 day syncs on the phone. It still took her 5-10 minutes for it to go away though. Since she switched careers from IT Engineering, she acts like she has forgotten all of the PM steps to adhere to with computerized devices. However it costs too much $$$ to upgrade her.
Here's what I did to (maybe) speed up the process. Go to Settings -> Developer Options and check the box for "Stay Awake." This will prevent the phone from going to sleep and should keep the messages loading or doing whatever ICS is doing that needs to be done for the messages to show up.
Also, once this process completes, it looks like its taking a long time for message threads with lots of messages to open as well.
Yeah I updated right before work this morning, the messaging app did that all day long until about 5pm and then it started working. Maybe it's a good practice to delete your text messages before updating to ICS