Well, this really depends on what you count as an engine. Technically, JOGL is an engine, which is used very frequently. Unity and UDK are also game engines, if that's what you mean. Plenty of games are made with all three of these options, along with other engines (so long as they are obtained legally), so it wouldn't necessarily be "frowned upon." Using these engines are almost always easier than making your own. For built-in texture/models, though, you need to be a bit careful with copyright infringement, because sometimes companies will give you those only for educating yourself with use of the engine.
As for making your own engine in Java, it can be moderately difficult to make a code-only engine yourself, and it will most likely not be as good as something like JOGL. These are generally more easier to adapt if you're using your own as opposed to something like JOGL. It really just depends on what your game needs. However, making your own engine with a user-interface takes significantly longer and is much harder, but it can be easily re-used and it is easier to start new projects with it.