My Eagle 2 balances perfectly with an OS-40LA, which is a rather light engine. A 4-stroke is heavier and you will probably need to mount it further forward to allow room for the throttle linkage. With a 4-stroke you will need to add quite a bit of tail weight. The 4-stroke/Eagle will be a heavier (and therefore faster) airplane - not really good qualities for a trainer.

I think you will become rather bored with the Eagle 2 fairly quickly after you solo (I did). You might consider a Goldberg Tiger 2 instead of the second Eagle 2. It is an easy transition from a trainer and quite a bit more capable.