I have done it on some bikes, not on others.
If a bike might be exposed to salt, I think it is a pretty good idea. My winter bike is not a beater, it is my Rohloff expedition bike. I frame savered it before I built it up. I have a pair of SPD shoes I wear in winter, other shoes in summer. The cleats on my winter shoes are a block of rust, and the other shoes have almost no rust on the cleats. Also the cleat springs on pedals that I use in winter are badly rusted. That is a pretty good sign of what road salt will do.
I bought an old Bridgestone a few years ago at a garage sale, it had been stored outside for over a decade, I am judging the storage period based on the diameter of the tree that was growing up through the frame. (Owner had to get out a sawsall to cut down the tree so I could buy the bike.) Took about a day to get the bad bottom bracket out of it, but once I did I found a lot of rust powder in it. In the chainstays there were some bits of rust coming out, but overall I felt that the frame was probably still sound enough to use as an errand bike. I have been using that bike now for years without a problem. Since I store that one outside I stripped it down and frame savered it. But in this case I would have had to strip all parts off anyway, every bearing needed grease, most plastic and rubber parts needed replacement, etc.
I have another bike that was badly abused and was often stored wet before I bought it. Much of the chrome platting on the exterior tubing was flaking off due to rust under the chrome. But the interior of the frame tubes where I could see inside looks great, that bike is a early 1960s Columbus tubing racing frame, the Columbus tubing appears to be naturally rust resistant.
But I have seen other frames that were carefully cared for and rusted out in a decade and a half. I think it is a roll of the dice if you got a frame that is prone to rust or not.
You need to move the frame around a lot to get everything coated, so if you do it you likely will want to remove everything off the bike first.
I never really know if I got enough frame saver inside each tube because the seat tube and head tube are the only tubes you can see inside to judge how well you got it covered. Also did fork steerer tube interior and I can see in there.
If you get framesaver somewhere you did not want it and find it later, like exterior paint, I have used coleman stove fuel to clean off the frame saver.
I like to let it sit for a couple days before I put stuff back together. It stinks, so I do that outside for the first day. Bottom bracket, I like to clean off the threads with stove fuel and then use grease on my bottom bracket instead. I don't want the frame saver to harden and act like glue holding things like that in the frame later.
I just frame savered a new frame a week ago, not because I expect that bike to get that wet, more because I just got it and figured why not? But if you have the bike assembled, then it is a tougher call.
Here is a new idea. When I received my Thorn Nomad frame a couple years ago (this is my Rohloff Expedition bike), I was really surprised to see inside the head tube that someone had put a piece of tape over the openings into the down tube and top tube. I had to remove the tape to get frame saver in there. At first I thought that was odd, but the more I thought about it, I thought it was pretty neat. It looked just like regular tape, like masking tape. Water can get into the the headtube by flowing down the outside of the steerer tube past the upper headset bearing. Then that water can go into (1) the top tube, (2) down tube or (3) out the bottom headset bearing and out of the frame. With that tape, that forced any such water to only go down out the bottom bearing and not into other frame tubes. I am not disassembling my other bikes to install that tape, but when I open up a head tube in other bikes for other reasons, I am adding the tape.
More info here:
The Velo ORANGE Blog: Frame Saving and Rust