Nope... freshwater bacteria and saltwater bacteria are two different beasts. A biological filter from a FW
tank will not speed anything up in a SW
Cycling a tank is getting that initial bacterial population in place - just like FW
. Letting it get established probably more has to do with introducing corals, or anemones. In my opinion, getting the tank established means slowly stocking the tank with fish (1 per month) and letting the bacterial populations catch up with the new bioload. During those first few stocking months, if it's not done slowly, water parameters will yo-yo as the tank tries to reach an equilibrium. That's not really good for corals. Giving the tank a few months to get "established" as you add fish, before adding corals, is what I think you're probably reading about.
In a nutshell, "established" can also mean stable.