So my group ran through the beginner game today, and it got to the part where they were allowed to wander around Mos Shuuta without too much incident, other than the wookie furiously beating a computer console trying to unhook the docking clamps while grunting and growling something about working for the imperials.

However, they decided to go off the beaten track and visit the warehouse. I thought they might go along with what was suggested in the adventure book, and take the Twi'lek along to distract Trex, but they decided to kill him and raid his warehouse instead. Not being one that wants to railroad, I let them do it, but decided the warehouse was full of junk save a handful of credits in an office. However, Lohwrick decided he was annoyed at the protocol droid that was showing them around after an alarm went off, grabbed a pole and shoved it where the sun don't shine. I did the customary melee roll, and the player rolled up 1 success, no failure or threat, and 5 advantage. I asked her what she was going to do with the advantage, and she decided it was her new droid on a stick weapon. Again, I thought about invoking GM fiat and saying no, but I took some advice from Order 66 and said "yes, and...", and what ensued was a rather hilarious battle with some guard droids, which made me glad that I allowed it.

My question is, since she's kept it and is now wandering around with a dismembered droid on her back, would it be too unbalancing if I started using it as a narrative device on coerce and charm checks on droids? I deliberately set its stats in a way that I thought would encourage her to put it down, but she was adamant that it was the wookie's new best friend, so I guess it's going to stay for the time being

A droid torso on a pole isn't going to make a very effective weapon and it seems you have made that clear through the stats you assigned. If she wants to continue using it let her.

As for coercion and charm checks vs droids. I might allow that for protocol and other non combatant droids but I doubt security and battle droids are going to be much impressed. In fact some droids interested in droid independance might actually be more angered than frightened by it.

I would use it more as an interesting plot device that comes up from time to time to create some funny or interesting situations rather than assigning it an actual static mechanical effect.

Heh... I'd give the droid the Scathing Tirade talent and have it unload on the players at the worst possible moments, like in the middle of a fight or when they're trying to sneak up on someone.

I really like that scathing tirade idea. The girl that did it told me it was too funny not to do, so having a rather pissed off droid that activates at inopportune moments would be something that would add to the hilarity of it all.