They can choose not to hire you for a host of reasons. It likely depends on what the arrest was for and if they can get any more information on it.
A fire background is not nearly as intensive as a peace officer background, so there is a chance that it won't pop up. But, depending on the depth of the FD's background, they might find an employer or past co-worker that will tell them about the arrest. Whether they will hold it against you or not will likely depend in large part on the nature of the allegations and how long ago they were.

