It use to be necessary to have vents in the top of heating units and have those heating units located under windows when the heating units were hot water or steam units and heated rooms through convection. Condensation was very important to control because most windows were single pane and “sweat” a lot.
Now with thermal pane windows and forced air units, the location of the heating unit (or in your case the direction of the grille) is not so important, because air is pushed around the room and does not rely on convection for heating. (Often heating air grilles are located in the ceiling.)
We now size heating units based on the number of air changes required per hour. Mixing air creates a more uniform temperature throughout the room...no “hot spots”.
Changing the direction of the grille will not significantly make the heating unit more or less efficient. However, modifying the heating unit to discharge upwards rather than horizontally can effective the efficiency of the unit and possibly void the warranty.