If they are already civilly married, then most likely they will be having a sealing in a temple. As a non-LDS/someone without a temple recommend, you won’t be able to see the sealing. I think that this is a standard experience for many LDS, since they know that sadly not everyone can see them get married for time and all eternity. As a groomsman, there isn’t a role for you during the sealing anyway, so you won’t be part of the ordinance (whether or not you’re LDS).
I was a groomsman for a friend’s wedding when I was LDS. I did get to see the sealing since I was endowed and had a temple recommend. His brother and sisters were not endowed at the time, so they ended up doing baptisms for the dead in another part of the temple while their brother and sister in law were getting married. As a groomsman, yes, I dressed up with the others, we took pictures with the rest of the party, had a bachelor party, pranked their post-reception car, and that’s about it. More people go to the reception than the actual sealing, so you’ll most likely do something there (though nothing religious). During the sealing, you’ll wait outside the temple with the rest of the people that aren’t able to go inside. The guests inside will come out, then the couple will come out (they have to change out of ceremonial clothing), and you’ll probably take pics outside the temple with the wedding party, family, etc.