I'm a hiring manager and the "just following up on my interview" email has never led me to hire someone. I have made a quicker decision about someone's candidacy because they followed up letting me know they had another offer (in the particular case I am thinking about, the decision was to tell them to take the other offer), and I have given candidates an update on the state of the timeline when they have followed up.
So if you want an update or have another offer, then sure, follow up. I cannot picture a situation where a follow up email would change the decision, though.