In the case of Unity, the free version is not missing any actual features, so what you want should indeed work for Unity.

I understand that Gamemaker(new 2.0) in the trial version doesn't limit resources, though you can only test, not release, in the free version.  In the past, they have limited resources(like only having 20 sprites, and similar things) in the free versions, but for the new version I don't think that is the case.  If I'm right, you can do the same thing as you can with Unity, except that for Unity, you could release with the free version if you wanted to(accepting the splash screen), while with Gamemaker you cannot release at all on the free version.

In my experience, if you a really wanting nothing but 2d retro styled games, Gamemaker is likely going to be better for you.  If you are ever interested in doing something with 3d, then Unity would be better, even if you do 2d now and 3d later, because Unity can do both(though 2d isn't as good for retro style games with Unity as it is with Gamemaker), but Gamemaker is really bad if you mess with 3d(it can do it, but you have to do lots of coding yourself for it).