Yes. This concept is called hardware overlays and there are varying levels of support for it in different GPUs and compositors.
There are tradeoffs. Using multiple hardware overlays may cost extra power and/or memory bandwidth, the number of supported overlays may be very limited, alpha blending may not be supported, and the transforms that can be applied to overlays may be very limited. The extremely hardware specific nature of the restrictions and the lack of good APIs exposing overlays means they get much less use than they should.