Nope, definitely not. That is wasted space. The back is for holding a backpack with a hydration reservoir. Anyway, I'm trying to gain strength and lose weight, not reduce my times by .02%.
Believe it or not, hydration packs have been shown to reduce aerodynamic drag for cyclists. There was a brief moment in pro cycling where riders wore them during time trials to shave a few tenths off their time. Strangely, the benefit of wearing one backward (on your chest) is a little bit better than wearing it on your back.
Needless to say, the UCI quickly banned hydration packs altogether.
They definitely did try both but I don’t know if anyone was ever cheeky enough to wear that setup in an actual race.
Currently they’re putting race radios in the front, centered side to side, during TTs. Rumor has it that the UCI has already had to tell a couple of teams to stop using extra tape and stuff to embiggen the radio lump.