Using unlocked iPhone internationally

If all goes well, no.   In my personal experience, it never has gone as planned.

Since you will possibly not be able to back up and restore while traveling, do it with your ATT SIM card before you travel.  

I had to erase, restore twice before getting the "congratulations, your phone is unlocked". Message.  It has taken some users multiple tries.

Interesting, thank you!  I will certainly unlock it before I go using my AT&T SIM.

If all goes well, when (and how) will the unlock message appear?

I have gone through the AT&T unlock process on a couple of iPhones in the past.  One of them never showed me the message indicating that it had unlocked, and the other did.  In both cases, I tested the unlock using a SIM card from a friend who had a phone on another carrier, and once I verified it worked, I replaced my AT&T SIM and everything was happy.

As for the iTunes backup/restore process, you need to keep in mind that it does not backup media synced to the device, nor does it backup photos/videos recorded on the device.  For both of those, you would need to use the normal media sync methods.  Another thing to keep in mind is that the Apple backup/restore process will not allow you to restore a backup on an older iOS version than the version where the backup was made.  This becomes more critical when you are replacing the phone, or if you are beta testing newer iOS versions, but it is good to keep that in mind.  In some cases, if you haven't performed an iTunes backup in a long time, it can take several hours to fully complete a backup, and in some cases, it may never complete.  I have yet to see any cases where a backup was successful but the restore failed, other than attempting to restore onto a device with an older iOS version.

Thanks, everyone, for your helpful comments!

I just finished erasing and restoring my iPhone.  It gave me the unlocking message first time... shows up in iTunes when I first plugged in the phone, and before it asked me if I wanted to restore it.

Restoration took a while, and a couple of aps required me to log in again.  But everything now seems set.

Did you forward your iPhone calls and texts to your iPhone with the UK SIM card?  If you did, did it work well?  If yes, how and when did you forward your US phone number to the UK phone number?  

I am asking these questions because I will be going to France.  I plan on buying a French SIM card and putting it in my iPhone so I would don't miss any calls or texts while I in France.

Thank you for your help.

Marty

@martyb11 You replied to a thread almost a year old, it is unlikely the OP will see this to respond. Just remember that if you forward all your calls to your Eutopean number, you will be paying international long distance for all those calls. You can not forward text messages.