I don't see why not. It's a 90 day max misdemeanor for making too much noise. It's not exactly a crime of dishonesty or an aggravated felony. However when you are asked in the application process disclose everything . The main concern is being caught lying.
You haven;t stated how long ago this incident was and that could be a factor. Assuming that there are no factual factors in aggravation of either the incident or your probation, this single incident should not be a bar to licensure. Mr. Kaman's advice about full disclosure is right on the mark.
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That will not be a problem. As long as you are felony free and have no financial related misdemeanor convictions (i.e. theft), then you will be good to go. However, you must disclose the conviction if the application for the license asks if you have been convicted of any misdemeanors. Failure to disclose the conviction may result in the denial of the license due to a pattern of deceit.
This reply should NOT be considered a legal opinion of your case / inquiry. At this time I do not have sufficient factual/legal documentation to give a complete answer to your question and there may be more to the issues you raised then I have set out in my brief reply.