Yes, it should. They look to be the same. I have a fitted a SW barrel in a SD and vise versa, but I have not shot either of the guns with that configuration.
I just recently acquired my first SD9VE. I have had SW9VE and other Sigma variants for years. Your question got me thinking so I took these pictures. They appear to be the same. They both fit in the other gun without any issues. I have yet to fire the SW barrel in the SD and vise versa. The SD barrel is machined with a slight taper that ends about 3/4 of an inch prior to the end of the barrel. The ends of both barrels are the same diameter.
Both the slide and barrel assembly of each gun will fit on the others frame without any issues. Both frames will dry fire the other guns assembly. I have not shot any live rounds out of either gun with this combination.