I have never tried this, but you are correct. The bacteria responsible for "cycling" are the same in freshwater and saltwater.
It would seem to me that you would have to acclimate the bacteria. Perhaps putting some gravel or the filter pad in a clean tank with identical freshwater (same parameters as the old tank) then gradually adding salt to the water, maybe over a period of hours or even days, until the salinity reaches the desired levels.
As said before, you will still have to cycle the tank and go slow. Remember too, that when you add LR you will have some die off on it and a small cycle will still occur. But this is a great way to get a jump start!
Once again I should say that I have never tried this myself.....I'm just guessing on the acclimation
Good luck!