I do enjoy eating guava fruits fresh off the tree. So do birds. Then the birds do what the birds do, and spread the seeds.
Wherever I've seen guava in Hawaii, it tends to grow in thickets that exclude other species, and it tends to spread. It is probably not as bad as miconia, but it's been around longer, and I don't think anybody is trying very hard to get rid of it.
By the way, if you decide to eat wild guava fruit, I'll pass on the advice I got -- don't look inside. You might to see some of the fresh protein you're about to eat...
For real information on guava, it's always helpful to look at wikipedia.