A trick I learned is to have a spring line tied off to the first piling you have access to while on approach. Have the length set so that you can drop it around one of your cleats, then leave the boat in forward/reverse idle (depending on how you dock) while you secure the rest of your lines.I suggest having your fenders out, as it will keep you snug against that side of the slip until you disengage the motor.
As before, each persons situation is different depending on dock, wind, crosswind, current, characteristics of boat, etc. Your suggestion is good for some conditions, but in the example (20 Kt. crosswind on either bow or stern quarter, depending on whether in fairway or slip). Approaching the slip with bow first, and having to make a 90 degree turn into/next to outer next (windward) piling to get into the slip, there is no time to do what you have suggested. Remember going forward at 1-2 knots, the cross wind is pushing boat sideways across the slip opening at about 1.2 ft./sec. while boat is also going forward about 2 ft./sec. Even manuevering to keep bow close to windward side of slip, the boat is going sideways at 1.2 ft./sec in a 14 ft. wide slip with a boat that is nearly 12 ft. wide. So the time we are playing with is just a few seconds, and there is no time to get to a piling to put on that spring line. The boat is just going down on that leeward outer piling no matter what, and at that point, you want to get it stabilized by stopping the boat so you don't drag the side against the piling and damage the hull or stanchions, and then getting fore and aft lines on that leeward piling. Use engine to assist to prevent boat twisting about this single piling and hold it there. As to jumping off to manually handle two lines from the finger pier is not feasible at that point because you haven't reached that short finger pier that is somewhere in the distance. So what is to be done at this point has to be done from the boat.
Now, to get the rest of the way into the slip is where your suggestion applies directly. On the windward outer piling, that I can reach using boat hook if needed, getting a spring line on the piling and leading it forward on the boat to a block on a cleat or through cleat, then leading the line to helm station where I can tend it (adjusting length as needed to allow boat to enter the slip by powering ahead). The temporary lines on the leeward piling are then released and taken in. Next, powering ahead against the windward spring line, using rudder to get boat off the leeward piling, and slowly entering the rest of the slip as springline is gradually lengthened is how I get it in the rest of the way. And as you suggest, use the springline with engine at low speed to hold the boat in position long enough to finish docking with regular lines.
In fact, over time, I have evolved my pre-docking procedure to have two lines, one on bow cleat, one on stern cleat lead along edge of deck so they overlap on the leeward side. (Lines should be loosely tied together or to life lines so there is no possibility of them getting overboard and tangled in the prop.) On the windward line, I preplace a springline at bow, one end led aft ouside the life lines to helm station, the other end led through a block back to a jam cleat at the helm station. And just in case I need it, a second line at windward stern cleat that I can tend from that end if I need it. Sounds like a lot of lines? Yes. But, I can remember at least two times when the wind got the better of the situation, and I had to make an unscheduled, quick docking in "first available slip" without any lines on deck. Genny sheets work wonders in an emergency.