if they are in a group you can move them all together at the same "speed"
to select the group use the hypergraph, outliner or push the up arrow on your keyboard (pushing up takes your selection up to the parent level in a heirarchy)
by grouping you give the objects the same pivot point and they will transform at the "rate", so they will move together, scale together, and rotate together, and they will die together

a boolean isn't going to work, and neither will combine because it doesn't make absolutely any sense at all when the two objects are completely different in every respect possible (polygons and surfaces are built differently)

if you don't like grouping (you'd have to change the pivot point after doing so if its not where you want it to be) you could parent the surface to the polygon, or the other way around, although unless your froze transformations then one will move "faster" than the other

another thing you could do is convert the surface into a polygon and then combine them from there