Not an easy answer, and temps are part of it, so the answer is...
If the temps are at or near freezing, and the rain is heavy, and the air aloft is warm (like our situation today), it can actually bring warm air down with it and melt the ice, because both the air and rain > 32°. If you've ever poured faucet water into a cup of ice and it melts, you get the idea.
However, if temps are lower and/or rain is not as heavy, it can be worse and add.
If it's pouring out, it doesn't necessarily mean more ice accumulation... only so much water can layer up in a given instant, the rest will run off to the ground.
But I don't think heavy rain is a good thing right now. And it won't be - until in many areas tomorrow morning, when it's been above freezing for several hours. In that case, it'll help scrub the trees.
Seems like an eternity to get to about 12 hours from now, though...