No, not really. The issue for training is not how fast the bike moves, but how much power you generate. You can train just as hard on a light bike as a heavy one, you just go faster for the same power output. And your maximum power, functional threshold etc. don't change because you get on a different bike. Or to put it another way, if you train at 400watts on a light bike you are working just as hard as if you train at 400 watts on a heavy one.
There is certainly a difference in feel. If you ride a heavy bike for a while, you feel as if you're flying when you go back to the light one. But that's just in your head, it doesn't mean that training on the heavier bike has given you any physical adaptations that you wouldn't have got otherwise.