As dumb an idea as this is, I'll field it anyway.
There's not much similarity between a pitcher and a quarterback other than they both throw the ball in their sports. I'm not going to waste time looking up numbers but I'm sure most good starting pitchers probably average 90 or more pitches per game. In football, 40 pass attempts in a game is considered a lot. They throw it a lot more in the NFL now than they ever have, so you see 50, 60 attempts in a game sometimes if a team can't run the ball for , but 40 is probably the average for a team that throws a lot. So 40 pass attempts vs 90 pitches, less than half for the quarterback. Given this information alone I'm going to say if you can't stay in an NFL game and attempt 40 passes, you probably shouldn't be in the NFL.
As for a relief QB, not every team is going to have two decent QBs. Some teams don't even have one decent QB. So pretty much what would happen in most "relief QB" scenarios is the defense would just blitz while staying in man-to-man with safety help forcing him into a stupid throw and probable interception. Unless the other team fields their relief defense, then it might actually work.
A better idea would be having a "between the 20s" QB and a red zone "QB," with your between the 20s guy being the "laser rocket arm" type and your red zone guy being the high accuracy type. But even this is pretty stupid because the QB position is about reading defenses and adapting to them so you wouldn't want two people playing QB on the same drive in the NFL.