Yes,but. It could work, but there are so many other products that are easier to use. Gentian violet can be very messy and will stain any it touches. I would recommend anything over the counter at the pharmacy over gentian violet.
No. No, topical medications have low success rates. However they are cheap with little risks. For someone with liver disease, you may want to try laser treatment (fyi I do not have any financial relationships with these treatments). Lasers studies have show success with effective treatment and sometimes cure rates but they are very expensive and no insurance company cover them. I hope this helps!