"Does it help in draining the last bit of fuel from a canister using the inverted position?"
No, gravity does not drain the canister, it is the pressure in the canister that is required to force the gas out through the jet in the stove.
The pressure in the canister depends on the temperature and the mix of propane/butane and the propane/butane mix depends on the starting mix and whether the canister has been used upright or inverted since full.
In short, propane and pressure are preserved when the canister is used inverted, propane and pressure are lost when the canister is used upright.
There is a whole article on this called "The Effect of Cold on Gas Canisters"