I don't want to serve coffee... or apply application hotfixes (stuff more typically "administrators" or "ops")... but at my pay rate? I'd do it and question why I'm getting paid $$$$$ to do something that $ can do.
If your boss is the sort of person who would serve coffee to the team you're probably fine cowtowing in this way. Otherwise, I think you risk being tainted in their eyes. They might see the others at the meeting as superior, wrt the role of programmer (etc.); and unconsciously associate you with less technical work.
I think you risk "why are we paying $$$$$, isn't that the guy who serves the coffee" even if it's subconscious.
I think this plays a funny parallel to SNL in 15/16 with Trump and Hillary... Trump played President on the show and Hillary played a bartender. (I may be off slightly on details, but the idea is there - perception is reality).
But my attitude is more along the lines of "I'll do what it takes to get the job done" and that attitude comes from my veteran experience - there was no shortage of times where the NCOs (mid level enlisted) would get "dirty" when a job has to get done...
You can see it as "why is that person relegated to nothing duties"... I see it as "that guy is part of the team and will get the job done, no matter what".
I do get your point and can see how "office politics" can spin things that way.
