That I don't know.
The thing is that the Gen 2 SW357V wasn't quite the same as the later Gen 3 VE models, but I don't know the extent of said differences. I presume that it would work because the barrels don't appear any different at a glance, but then again, Glock barrels nor M&P barrels look all that different at a glance either, and dispite what some folks on the internet claim, Glock barrels will not in fact function in a Sigma.
That being said, it probably isn't a good idea to go shooting .357 SIG out of an SD40VE regardless. .357 SIG Conversion Barrels may be popular aftermarket options for a lot of .40cal pistols, but the fact of the matter is that the .357 SIG operates at significantly higher chamber pressures compared to .40 S&W, ergo it takes more than a mere barrel swap for an ordinary .40cal pistol to handle a steady diet of .357 SIG.
For reference here, the .40 S&W operates at a peak chamber pressure of 35,000psi as per SAAMI Specifications, whereas the .357 SIG operates at 40,000psi, and 10mm Auto operates at 37,500psi. In other words, .357 SIG operates at even higher pressures than even the mighty 10mm Auto.
Furthermore, it's worth noting that the slide weight of the SD40VE is considerably lighter than that of the SW357V, meaning that if you fired .357 SIG out of a SD40VE the slide velocity would be higher, which would need to be compensated for with a heavier springs to help reduce said slide velocity.
Last but not least, keep in mind that the M&P357 was taken out of production after several trips back to the mother ship due to issues that Texas Rangers were having with the pistols which S&W was unable to resolve, and the M&P is a more robust design than the Sigma Series to begin with.
In closing, if you want to shoot .357 SIG, then I would sooner recommend investing in a SIGsauer or even (dun dun duuunnn) a Glock 31/32 than trying to track down a SW357V barrel and hoping that it will function as a drop in part for a SD40VE. Trust me, I would love to be able to convert my SW40VE to .357 SIG myself and even looked into the matter myself, and this was a conclusion that I reached based on my findings.
Hope this helps.