It depends on what you're looking to get out of the experience.
Personally, for me, I was a huge Harry Potter fan so I read the book immediately when it came out. I adored it, but I know a lot of people weren't huge fans. That said, I think it's definitely easier to read if you have a theatre background, which obviously everyone on here does. So I think most of the people who didn't enjoy it didn't know what to expect out of a script.
One downfall is that you will probably have an image of the characters in your head. But I guess this could be a good thing as well. I know for me, Sam's portrayal of Albus very closely align to what I would have done with the character. But Anthony's Scorpius is pretty far from what I imagined (albeit absolutely brilliant! Seriously, this kid deserved the tony). It was a bit upsetting to me when the character went in a different direction than I had though, however, and I obviously wouldn't have had that issue if I hadn't read the book first.
On the flipside, I think reading the book has helped me not get too attached to one actor. While I'm going to be devastated when the original cast leaves (Seriously, Jamie Parker IS Harry Potter), I also think it would've been worse if I had based my idea of the character on the actor's portrayal.
But again, this is coming from the perspective of not only a theatre fan, but a HUGE potterhead. If you're a more casual fan, I'd probably just watch the play first.
If you're talking about the original 7 books, as long as you've seen the movies you'll be able to follow along with the play. Although there are some small references that you might not get, because they either mention events or characters that only appear in the books. These, however, are all very minor. There's also a summary of each of the 7 books (more or less the big events that happened in them) in the playbill, so if you absolutely haven't seen or read anything, the play will make sense, but you definitely won't get the full experience.
Sorry for the tl;dr. Just wanted to give a very thorough opinion :)