Will wearing a backpack on my chest make any difference on my health?
I am not aware that wearing a backpack is bad for your back when cycling. I've been doing it every weekday for the past 8 months without ill effect. Perhaps if the backpack is very heavily loaded it's different. I do know that a lot of people just don't like wearing backpacks when riding.

Wearing the backpack in front seems like it would put loads on about the same points on your skeleton as wearing it in back, with the added problem that it would interfere with your legs' movement unless you're in a very upright position.