Join Date: Aug 2011
Location: Barcelona, London, on a plane
Programs: IB+ Gold, TK E+, Hyatt Globalist, Marriott LTP, IHG Diamond
Posts: 14,211
No, you cannot do Hola Madrid on award tickets.
You also cannot do stopovers on award tickets. Well, you can... but by booking separate tickets. However if you needed "married segments" in the first place, that award space will disappear when you look for the direct MAD-USA flight.
So it's not a good idea to book a trip and then call back to delay the TATL flight by a day or two.