Okily!!
As it happens, this situation arose after TWO convoys (one passing each way through the strait) came through. Each had a troop ship I sank.
It's funny: if you look at Kerch on Google Earth, you'll see there is really only one channel VERY close to the city which could be used for deep draft vessels. Presuming things were about the same in March of '43, I don't think any Soviet ship would be passing through (save for the odd sub) as Kerch is still in German hands and would certainly have the guns to pwn anything in the near channel.