I don't think that's best idea because you would take away cooing from VRM section which is right between CPU and exhaust place/fan. Just CPU cooler fan may not be enough to take all the air out of the case. Total effect would not be any better than not having backside fan at all.
This! a hundred times this! People focus on cpu heatsinks to much and too little con case cooling. Want a tunel? create a WIND tunel with exhausts and intakes (exhausts in the upper part of the case, intakes in the lower part) control them via software that matches temperature to fan power and it will be silent enough when not under high load.