You can take any available connection within the connection window. Example: I have an LHR-AMS booked on BA, I had options of a 100 minute connection or a 3.5 hour connection from my flight arriving into T3 (LHR-AMS departs from T5). I chose the 3.5 hour connection to give myself plenty of time to get between terminals, and I'm EXP (Oneworld Emerald) so I can access the F lounges anyway if everything happens to go smoothly.

If all BA LHR-AMS flights within the connection window did not have availability, then I would have to take the first scheduled LHR-AMS flight outside of the connection window. If that flight also did not have availability, then I would either have to make my LHR visit a stopover (and find a still later flight with availability), or I would be unable to book the connection. If the next scheduled LHR-AMS flight was more than 24 hours from my arrival at LHR, then I also would not be able to book it as a connection, even if it had award availability.