No... all calibers use the same springs in the current version of the Desert Eagle Pistols. (Mk XIX)
The springs of the Desert Eagle aren't caliber specific "recoil springs" in the conventional sense. The gas impulse is somewhat regulated by the size of of the gas port, and the gas pressure generated by 357,41,44,429, and 50, are all about the same operating pressure, somewhere in the mid to upper 30K range.
The point being that the springs on the Desert Eagle are dealing the slowing down the slide at a similar velocity regardless of caliber, and their primary job is getting the next round from the magazine into the chamber.
The reason the Spring Tune Up kits are different for different calibers is only because of the Magazine Spring in the kits... it is different per caliber. As far as I know, all other springs are interchangeable.
One last thing... the springs are usually good for at least 1000 rounds. When you first put a new set in, don't panic if they are a bit stiff. Just be sure they are very lightly lubricated. The primary (the multi-strand spring) when completely dry can bind just a little bit and does require about a 40 round break in to get all the strands seated and running smoothly. Operating the slide manually can take care of some of it, but doesn't seem to be as persuasive as shooting it. I have been meaning to demonstrate this with a scale to pull the slide on a new spring set vs a 40 round set, as it is enough to be perceivable by hand on a gun with polished slide rails. In my 25+ years of trouble shooting Desert Eagle issues, the springs are usually the last issue. It is almost always a dirty gun. I drop the slide and wipe the inside of the frame under the springs and the slide rails about every 50 to 100 rounds, as so much dirty powder is blown through the gas system and under the barrel.
Good luck with the conversion set!
MrBlackCat