That's definitely a way to temporarily offset your reload penalty and gain about 6 double reloads worth of DPS (about 72 seconds as each pickup/reload/replace takes about 6 seconds). But in the grand scheme of a full horde night that's going to be a drop in the bucket and it requires alot of space.
TBH this sounds infinitely more useful for non-turret spec than it does for turret spec because non-turret specs are the ones who suffer the most from the reload time since they outdps the turrets by so much. Turret spec would prolly prefer 4 turrets and always be reloading 2 turrets while the other 2 are firing. No way I'd do this without keeping rows of junk turret ammo in a chest nearby though. I'm planning on bringing 5,400 junk turret ammo to the Day 26 horde as it is. If I was to do this I'd bump that up to 7,000 and it still might not be enough.
Not to mention that this makes the "gameplay" in turret spec would literally just be 20 minutes of doing nothing but reloading

. The amount of downtime you spend manually reloading turrets already kind of sucks even maintaining 2 of them.
*Edit: I'll do it for my next horde defense. I don't promise to enjoy it but it'll prolly amuse those watching the video at least. Now to farm all that iron :X. 4 Turrets, reloading always the empty ones to keep full turret uptime.