If I add a reflector(mirrors etc.) to the light hood of a 15 watt lamp,

does that means my watt per gallon for my tank had doubled as more

light is being directed into the tank?

I don't know about the exact wattage that would reach your tank that way, but it seems like there will be somewhat more wattage going to the tank, yes.
I have a double stand of 75 gl tanks in my house, the lights being on the upper tank. The funny thing is that the upper tank only has brown algae, which basically means insufficient lighting. The lower tank, being further away from the light, has green algae on the glass!
I found out that the bottom of the upper tank, being glass, reflects more light to the lower tank, therefore the algae grows green there. Puzzling, isn't it?

hmmm......interesting.....