Should home health aide apply pressure to a profuse bleed?

Generally speaking, yes. It is what is taught in basic first-aid classes.

I am unsure what the significance of asking about a home health aide applying pressure is. If your concern is that the aide isn't properly educated to apply pressure to a bleeding wound: they may be. Most home health aide agencies train their staff in basic first aid and CPR. Applying pressure is the first thing to do to control bleeding after assessing the situation to be sure it is safe to do so and that you are capable. If the aide assessed the situation and decided for whatever reason NOT to apply pressure then he or she shouldn't have, provided their assessment was sound. Generally speaking, if the aide is trained in first aid and they are on-the-job and it is safe for them to do basic first aid, then they are bound by their agency's policy to do it, assuming the patient gives consent. (Unconsciousness, in this case, would be consent.)