If your mile of cable is perfect, no joins, no discontinuities, then in theory the mismatched source drives the cable, and all the power is completely absorbed by the load at the far end, because there, it is perfectly matched.
Thylacine is quite correct in that, and you get to claim your +6db prize.
However... if its not a perfect system, and there are impedance humps and bumps, anything reflected back at the source along the way, is going to be reflected with a vengeance back down the cable to the load.
There will be a delayed echo opposite in phase to the original signal.
It might all work perfectly well, there is no real way of knowing for sure without some testing.
.
What I would do, is get my hands on a TDR (time domain reflectometer) and test that cable.
If its as smooth as a babies bum all the way, you can then be almost certain it will work with a mismatched source.
If there are any reflections, you can measure the db return loss, and the time delay will tell you the distance to the discontinuity.
At least then you will know if there are going to be any reflected echoes and how far down they will be in db.