I don't see that there is a prohibition against tremolo in Irish music for mandolinists. There are so few (mandolinists, that is) to begin with and you can't hear them in a session (where the majority are) so it is probably a moot point. I think that judicious use adds a lot to the music, especially in a band situation, but it is a limited technique that a lot of payers can't do well.
That being said, there is no reason not to use it and see if it makes your playing more musical. I think that most of the time there are better choices when trying to play a sustained note that works better with the tradition but it has worked for other styles.
There don't seem to be many mandolin police out there and mandolin is in an early phase of development for Irish music (more advanced for Scottish, it seems) with a lot of exciting stuff ahead. Tremolo deserves a try.
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