Yes the 637 (Sturgeon) class is driveable using SCU.
You have to run scPlayableSubChanger.exe (the main component of SCU), then simply select Sturgeon_1975 or Sturgeon_1985 from the list and click the "change" button.
Then, and only then, can you select it as a playable for missions, or in the mission editor. (If it's not enabled, the "playable" check-box won't appear.)
And of course, in case anyone doesn't know, SCX/SCU (both required) are available at Bill's site
http://www.subguru.com. Go to the downloads section and scroll WAY down to the Sub Command header. I haven't installed this in ages so the only advice I can give is read the installation instructions carefully and follow them. I remember there was one step I always seemed to miss about running one exe or another

but just read carefully and it should go fine.
-UB