I can't give a definitive answer, but here is our experience. We were in Europe (including Ireland) 6 weeks ago and set both our iPhones to airplane mode with wifi enabled. I set my phone to manually adjust the time wherever we were. I asked my wife if she wanted me to set her's and she said no. Well, every time we had wifi, her phone would auto change times.
The alarm is going to be based on the time showing on the phone, so it has to show the local time to work correctly.
That's a great question, Jam1128. We understand how important it is to have access to your Alarm while traveling, but as long as you have your device set to Automatic date and time you will have no issues here.