My current show is a musical with some pit musician and some actors playing instruments (electric guitars, basses and drums). The pit guitar player tunes and maintains the 12 guitars/basses and the pit drummer maintains the drums. If a string breaks mid-show we have a "Swing musician" who can drop out of most numbers if necessary (he mostly doubles) to change and we have a back-up guitar we can use in a pinch. Other than playing them onstage, the actor does nothing. Probably not at all helpful for your situation.
Another musical had an actor playing guitar onstage. We actually ended up renting his guitar for the show. He tuned it during half hour (even though we had pit musicians, a prop guy, a stage manager and a sound head all capable of doing do) and maintained/changed strings as necessary. I'd say if we weren't using HIS instrument, he probably would have had us change strings but he still would have tuned the guitar - sort of like an actor checking his own props.
In both shows, sound checked the packs on the instruments in hour before half.
I don't know that you'd need an amp to tune. We use the guitar tuners that clip on - accurate, fast, and easy.
Hope some of that is helpful to your situation.