Hi Doug,
You won't be able to paste it into the integrated project schematic, you'll need to paste it into the integrated project layout. But yes, as long as you have ECO mode enabled in the integrated layout then it is literally copy the part from the non-integrated layout into the integrated layout. Right click the part in the integrated layout and choose Save to Library and you should be prompted to choose which library partitions you want the part and the decal to be copied into.
-Travis