There is no clear cut answer here, there are so many variables but…..
if she is a mature 19 year old (and it sounds like she is) and
if you are comfortable with having him in your home
then I would say yes. She is an adult now and responsible for her own decisions. She has respected you enough to ask the question rather than take it for granted, and I would respect her enough to allow her to make her own decisions and mistakes and be there to support her when those mistakes are made.
Waiting with bated breath now to find out what bon-bon said!