Is it possible to compile a collection?
Indeed it is. Once you open the main compile overview window, on the right hand side is the Contents tab by default, where you can see what will compile. At the top of that is a dropdown where you can pick a source to compile (by default the entire draft folder). You can select your collections, including search results, from the bottom of this list. Also note the “Current Selection” choice, which is very useful if your mainly using collections to pick out three or four chunks of the draft folder. You could instead just select them and then compile with that setting.