OK, something about this high level minion discussion doesn't sound right. On one side of the argument, it seems as if that low level replacement PC immediately runs into that big baddie. When does this ever happen? Most big baddie lairs have a lot of lower level creatures around (the dragon's territory, etc). By the time the low level replacement PC even runs into the big baddie itself, he or she won't be so low level anymore, so it seem the entire discussion is moot.
It depends on how the DM handles leveling. I've seen systems of no more than one level per day, or the PC gains all of the levels overnight. Other DMs might do it after a short rest, or even after the combat is finished.
I.e., even if you had a 10th level party pick up a 1st level PC, the way adventures are structured, the party would most likely get enough XP to hit level 11 before the finale. XP to go from 10 to 11 is roughly the same as going from level 1 to 7. So a 7th level PC in a party of 11th level PCs doesn't necessarily need to just pick off the little guys.
Even if the DM hands out XP immediately, a party could go in, wipe out most of the minions, have two PCs die, go back in the next day and the new PCs are level one.
Every situation (and table) is different.