Will stopping the use of minoxidil make me lose hair even if I don't have androgenetic alopecia?

Minoxidil is an anagen promoter.  If you cease using minoxidil, you could have a slight shift toward a higher concentration of resting or telogen hair.  This might be evident by a shedding at some point perhaps in a few months.  However, if you don't have androgenic alopecia, you really should not experience thinning or balding.  

This is a great question. The answer is “maybe.” If you don’t have AGA but are in the very very earliest stages of AGA, a shed could occur and the result be hair loss. Also, if minoxidil is benefitting some sort of telogen effluvium you have (even if subclinical)... you might still get hair loss from stopping. This includes a telogen effluvium from stress, seborrheic dermatitis or poor diet. No, the body does not really become dependent per se.

If you have taken minoxidil for a long time and developed hair that is dependent upon it, then when you stop the drug, the hair will fall out that is minoxidil dependent