Humans aren't good judges of how often they dream. You have REM sleep several times a night and generally if you're woken up during REM sleep you will say that you were dreaming.

It is probably more likely that you are simply remembering dreams more when you can hear rain on the roof - either by power of suggestion, or because the stimulus of the rain noise is noticeable and memorable in your dreams, or because the rain itself is waking you up.

This isn't to say that you're wrong - there most certainly is an effect - but whether that effect is positive or negative is unclear.

I too sleep with earplugs in I've noticed something similar. When I take naps during the day and I use the plugs I find that it is the best sleep I get, I feel super refreshed. During the night when I sleep with earplugs in I usually don't sleep as well as I would without them (minus the loud roommates). But I am a side sleeper with a memory foam pillow so it tends to cause some pressure on my ears for prolonged sleep periods.