Well, yeah, a pretty good swath of UDRP cases involve a domain registrant in one jurisdiction and a trademark claimant in another jurisdiction, and I've handled hundreds of those types of disputes. So, as mentioned above, the specifics matter, as well as "what kind of a problem are you concerned about?"
For example if someone has a trademark in Nowheristan and they get a default court judgment against you in Nowheristan and then send that to your domain registrar, then what actually matters is "what does your domain registrar do if they receive a court judgment from Nowheristan?"
If they file a UDRP, then a number of things are going to come into play. You didn't mention whether your US TM application is an intent-to-use or use-based application. Obviously, if it is a use-based application, then you are already using the domain name and presumably have evidence of that use. A UDRP panel is going to look at the credibility of your trademark filing and whether it reflects actual bona fide use of the domain name for whatever goods/services recited in the filing, or whether it simply looks like a dumb stunt for attempting to get around the UDRP. LIkewise, if it is an intent-to-use application, then it may, in combination with other evidence, support a showing of substantial preparations to use the domain name for a bona fide purpose.
So, yes, there have been quite a few cases where someone had a registered trademark somewhere and nonetheless lost a domain name in a UDRP in circumstances where the panel believed the trademark registration was simply a fig leaf to get around what struck them as cybersquatting.
https://www.wipo.int/amc/en/domains/search/overview3.0/#item212
2.12 Does a respondent trademark corresponding to a domain name automatically generate rights or legitimate interests?
2.12.1 Panels have recognized that a respondent’s prior registration of a trademark which corresponds to a domain name will ordinarily support a finding of rights or legitimate interests in that domain name for purposes of the second element.
2.12.2 The existence of a respondent trademark does not however
automatically confer rights or legitimate interests on the respondent. For example, panels have generally declined to find respondent rights or legitimate interests in a domain name on the basis of a corresponding trademark registration where the overall circumstances demonstrate that such trademark was obtained primarily to circumvent the application of the UDRP or otherwise prevent the complainant’s exercise of its rights (even if only in a particular jurisdiction). Absent evidence of such circumstances indicating pretext however, panels have been reluctant to reject a respondent trademark registration out of hand.