Yep. I've used several brands of the "Gotoh" style that fit fine.
mech
Edit: I recently had a string that would slip and go flat while playing. Upon removing the string from the tuner, the wraps of the string were broken at the bend where it goes in the tuner so only the core was supporting the tension. Checked the other strings and found one more that was in the process of doing the same. I'd check that before ordering a tuner. FWIW...the most common (although it's uncommon) failure of a mini tuner is for the "nub" on the post that goes into the gear to break. This normally leads to the string going immediately slack.