Yes and no.
If your beer is fermenting away, CO2 will be keeping plenty of trub from settling, so if you try dumping while fermentation is on the way, it won't be very dense and you'll lose some beer.
It'd be much better to cool it down after fermentation is done, then trub off 24 hours after chilling, then take yeast off 36 hours after the initial chill (and then again 24 hours after that).
Unless you have the trub sat in there for a a long time or you are getting a lot of break material and hops from your kettle into the conical, it shouldn't be much of a problem (unless you're trying to make a nice clear beer like a lager, pils, hefe or kolsch for example, in which case the less trub and yeast the better).