imparfait/passé composé distinction

Yes, the meaning would change. The difference -- to French ears -- sounds like this:

J'ai toujours rêvé... -- I've always dreamed...
Je rêvais toujours... -- I was always dreaming...

The passé composé stresses the fact that there was a string of successive, individual events in the past. The imparfait makes it sound more like a  state of dreaming.