Yes. Even better is to trade your Eevee to Emerald and feed it berries (#21-#26) to make it happier.
Don't forget, you can have your rival's sister groom your lead Poke, I think every 100 steps. Sorry, I haven't took the time to count steps. She will groom it and then tell you whether it is happy enough. Once happy, trade to RSE and level it up.
BTW - I answered this before in the Simple Questions thread. Make sure to ask your questions like this there from now on.