In theory, yes, in practice, no.
The MP-38 was manufactured from 1938 to 1940, after that it was replaced (in production) by the MP-40. Although there were an additional 12,000 assembled during 1941. Total production numbers are somewhere around 52,000.
From late 1940 to early 1942 (anything after early 1942 is unlikely to have arrived at Stalingrad in time) Germany produced roughly 200,000 MP-40's.
This means that roughly one in 5 MP's produced up to that date was an MP-38. For units in constant fighting from early 1942 to Stalingrad (as was the case with most units in and around Stalingrad) it's unlikely that any of the MP-40's produced from early 1942 onwards would have reached them.
Remember that if a weapon is produced it's going to spend some time in a warehouse somewhere in Germany, then it would be shipped off to the east, spend some more time in a warehouse, then be shipped towards the front, spend more time in a warehouse, be handed out to a Division in the reequipment phase, spend some time there.
Generally, I'd guess that one in 4-5 MP's would have been an MP-38 for units in Stalingrad.
Now, the only problem is that all but early production MP-38's are nearly indistinguishable from MP-40's.