Nobody stops you to configure hibernate with vertx, yet I wouldn't do it for a production based code.
Vertx's power is that it is light and non-blocking. Hibernate is neither. So building vertx with hibernate, would strip away vertx's advantages.
Anyway, if you really want it, I have a sample of configurating a vertx-spring-jpa-hibernate-rest services (I did it just to experiment spring more with vertx) and I did some load tests on top of it (don't recall the results, but they were better than tomcat).
Honestly, I would recoment JOOQ for vertx. It fits like a glove.
Here is why:
Jdbc is blocking. Any request to database via jdbc will block your verticle. Unless you make it a worker. In that case, you do not have much to win or gain.
Hibernate is a full ORM bloated framework. It has high overhead in terms of performance, and is also blocking (using jdbc)
JOOQ can very easy map results from sql queries into directly a dto. No longer ORM problems that you must do a conversion manually to business objects.
JOOQ is a lot of fun to work with. It is light, and can be used with fibers, which is non blocking. Fitting perfectly with vertx :).
As an example, you can start from here: