Hobow: Not in my opinion! I shoot Widows, Drakes, Bears, Wings, Howatts, Hoyts, and others from the 50s and 60s all the time. And, a lot of them with strings that might surprise you! Have for 20-25 years. Yes, it's wise to watch for problems.....same as with cedar arrows, or a lot of other things. Keep your "lady" on a pedestal if you want. I don't. I want to see what they can do -and it's a lot!
Now, to your original question: yes, phenolic tips can be reglued. I wouldn't worry about it until they separate.