FlyerTalk Evangelist
Join Date: Aug 2011
Location: Barcelona, London, on a plane
Programs: BA Silver, TK E+, AA PP, Hyatt Globalist, Marriott LT Plat, Hilton Diamond
Posts: 13,043
You would need just about everything to go right to make that connection, but in theory if you were connecting Vueling to Vueling (domestic or Schengen) you could get off the plane (assuming you don't get stuck with a remote stand / bus), find your next gate and rush over there (no passport control or additional security).
If you're trying to connect different airlines (particularly low cost carriers who are in the old terminal), the Madrid Puente Aereo, non-Schengen international... no chance...