Can taking 1mg of Finasteride a day impact body/beard hair growth?

Hair loss has many causes, including stress, medications, autoimmune, genetic, trauma, etc. Medical treatments can work and options would include finasteride (propecia), minoxidil (rogaine), PRP (platelet rich plasma), laser light therapy, and vitamins. It is often uncertain which medical therapy will help which patient and so a combination of therapies is typically recommended to maximize benefit. A hair transplant is a surgical option and is appropriate for certain conditions and individuals. 
The goal of a beard transplant is to provide fuller coverage while preserving a natural appearance. An assessment takes into account such factors as the apparent thickness and curl of your donor hairs, the color contrast between your scalp and hair, your hair loss pattern, your age, and many other factors. The state of the art technique is FUE (follicular unit extraction), performed with a hybrid blunt punch that minimizes graft transection while allowing for the use of the smallest possible punches to minimize donor site scarring while maximizing regrowth.
In your situation, the Finasteride might help you maintain your beard it would not lead to it falling out faster. Gary Linkov, MD
Hair Specialist
Manhattan

Finasteride decreases DHT concentrations in the serum and the scalp by up to 70%. Lowering DHT levels in the scalp reduces its harmful effect on the scalp hair follicles.However, beard and chest hair are stimulated by testosterone and DHT. Finasteride might reduce hair density in these regions, although reports and studies suggest it only has a minimal effect.

Yes, you can take finasteride 1 mg every day and few men report negative impacts on their beard growth.