I apologize for the short reply I made this morning, I'm sure it wasn't helpful
Assuming we're still talking about a 1000 ft thick cloud layer, yes given these conditions you'd be unlikely to get in trouble.
There's a couple of factors to consider; the expected rate of accretion and the exposure time. Let's assume your airplane is capable of climbing at a rate of 1000 fpm clean (ice free). Depending on conditions your normal (clean) climb rate can degrade rather quickly if you start picking up ice but it's hard to imagine in the conditions you describe that you wouldn't be able to climb on top of the layer.