If a baby who is a Bechor had his Bris delayed to the 31st day, and now on the 31st day he is ready to have his Bris and it is also the day of his Pidyon HaBen - which Mitzva should be done first? Do you do the Mitzva of Pidyon HaBen first as it is its proper time or do you do the Mitzva of Milah first as it is the foundation of the Jewish people and without this covenant between Hashem and Klal Yisroel there would be no Mitzva of Pidyon Haben?
Shach (Yoreh De'ah 305:12) discusses such a case, and writes that the circumcision should be done first, for the reason you mentioned: the mitzvah of pidyon haben exists only because there's an existing covenant between Hashem and us.
However, R' Dov Aharon Brisman (what an appropriate name for this discussion!), the rav of Young Israel of Elkins Park, argues that in a case where the time for the bris comes out later on the 31st day (which can happen if he had some systemic illness, for which halachah requires a full seven-day waiting period - 168 full hours - after he's pronounced healthy), the pidyon haben should indeed be done first, because its time has already arrived.
The Noda bihuda discusses some whose practice was well, once the bris is postponed, we might as well postpone it a few more days; he strongly rejected this. Taking it further, the Dvar Avraham (1st chelek) rules that if, for whatever reason, circumcision can't be done on the eighth day, then the clock is ticking and it should be done at the soonest time available (during daylight hours, assuming a healthy baby and a qualified mohel) - every delay is another passive violation of the commandment. (Rabbi Hershel Schachter shiur on Vayeira mp3).
If that's how we rule, then it should be simple to deduce that circumcision comes first.