^Only if they still reside in that territory. And even then, there are legal ways to allow yourself to vote. If you've ever lived in a State, for example, you can still vote as an absentee of that state, even if you've been living overseas in a territory for a very long time.
I've never done it just because I don't want the IRS climbing up my ass, which those nazis have already done twice just because of a few accounts that still had my parents address listed. But I have several friends who have.
So yes you could run for president if you were born in a US territory, live in that territory, vote for yourself, but your fellow territorial residents would not be able to, unless they had previously lived in a "state" and jumped through the necessary hoops in order to do so.