I'm 18. Will I keep a beard grown by Minoxidil, if my genetics would have grown it anyways?

The simple answer is yes-  the hairs that minoxidil will potentially stimulate to grow will continue to grow after you stop the minoxidil.

The
best way to judge when and how your beard will fill in is to ask the male family members when
they started to grow beard hair.  Minoxidil
works by helping you keep the hair you have. 
If you don’t have the hair yet, you have to wait for the hormones to
kick in to first give you beard hair.

Minoxidil has no evidence to start or stimulate beard growth , but you would better to wait for beard growth untill 23. If your family man have same problem , that means you would have same type of lack of dansity in beard . Eventually you may have a FUE op for beard restoration anyway.

Many young men want to accelerate their beard growth and ask about it. It takes age (genetic triggers which occur in family lines) so if you want to find out when your beard will grow out, you need to find out when your father or grandfather started to grow their beard. Hormones should have kicked in nicely by the time a man reaches 18 but he must wait out his genetics as hormone alone are not responsible for the onset of beard grown. Beard transplants can be done when the young man is a bit older (over 25) if the beard has not grown in yet. Minoxidil may help and if it works, then you are among the lucky few