Yes, this is possible. Copying and pasting is unnecessarily complicated in Eagle since they don't use the standard shortcut keys and whatnot.
You basically use the group select to select the components, nets, etc. and then hit the copy button then CTRL+right click on the group. At this point you will be dragging around the selected group. Hit escape since you don't want to drop it back into the current schematic.
Now pull up the schematic that you want to paste into. Click the Paste button. Drop the group on the schematic.