Don't see why not. Very good and very much an under rated cartridge. I've had 5 different rifles/pistols chambered in 358 Winchester. I have a Winchester 94AE in 356 Winchester(lever gun sister of the 358) that I like very much.
The model 38 (as in 1938) is a model 98 Mauser. The Turks did two things differently. One: they extended the length of the receiver ring about 3/16" and it is that much longer than a Mauser M98. Two: The front ring is threaded for the small ring barrel. Meaning that Swedish M96, or M38 (not the same rifle) barrel will fit the threads cut into the receiver. The Turkish M38 is not small ring as it is the same external diameter diameter as the M98 but internally it is a small ring, or more correctly, small thread. Technically still classified as a large ring M98 Mauser. The original 1903 models were in 7.65 x 53 but were rebarrelled to the 7.92 x 57 (8x57) and all of the M38's were 8 x 57 Mauser.
Now, to your question. Yes they would make a great action for a 358 Win. They were made in the in the 30's and 40's and are of good material and design. I would see no problem with them in that chambering. When you order a barrel inform the supplier that it is a Turkish (small thread) Mauser and you can have it threaded to fit. Your smith can either cut the flange in front back or leave it as is. This action wouldn't need any follower or rail rework to feed the 358 smoothly. Great round, the 358 Win. I have a little M70 carbine in this caliber. Just lovely. Good shootin'.