I'm not familiar with actual NYPD policy, but...
Can a cop go straight from Detective to a higher rank like Lieutenant without becoming a Sergeant first? I always thought that it was like the military, in that you would have to progress up through every rank and not 'skip' any.
As for Benson: I'm sure the writers could come up with an excuse to place her at a higher rank. I think she'd do all right in running the squad, but would probably not want to be stuck behind a desk all the time. This is why, for example, Jack Webb ignored Joe Friday's promotion to Lieutenant (which happened at the end of the original Dragnet
series) when Dragnet '67
started: the reasoning was that few lieutenants get out into the field.