IMO, it depends mostly on how much you are going to use it. If you're talking about 100ft of crown molding and that's it, then I would say no. If you are going to have a regular stream of projects, then yes.
5 years ago, I was in your situation. I had never used anything but a brush and a roller. I had a contractor replace 8 interior doors in my house, and he wanted $1100 to paint them (doors and jambs). I took the plunge and bought an HVLP. It was a great move. On newly installed trim etc., you will get a professional look.
A few things to consider, however. You are probably talking about latex "enamel" (rather than tinted lacquer) I presume. To spray latex, you need a 4-stage turbine. That plus a good gun will run you around $1000. Stay away from anything less. A lower powered unit might be fine for lacquer or shellac, but you'll never get a decent result with latex without a 4-stage turbine.
Don't expect to save much time. It is just that the nature of the job changes from "painting" to "prep and cleanup". You will have to mask off *everything*, because there is a lot of overspray.
Don't expect to paint walls or ceilings with HVLP. HVLP moves
1 quart of paint in maybe 10 minutes, and large area surfaces are impossible to spray and still keep a "wet edge". If you want to paint walls, rent an airless sprayer.
I am very glad I got my HVLP. I have slowly been renovating my house, one room at a time. I've done crown, window molding, door molding, and plenty of cabinet finishing. I've sprayed latex, lacquer, shellac, and catalyzed conversion varnish. When I compare my actual total time to hiring a pro, I end up paying myself $50-100 per hour.
So, if you want to approach this as an ongoing hobby, then go for it. If you'd rather be playing golf, then hire somebody.
If you do go the HVLP route, I am very satisfied with my Fuji Q4. It does a beautiful job, I have never had a problem, and when I have bought supplies and accessories I have dealt direct with the factory. The owner answers the phone, he is a nice guy, and is very responsive.