Stalin's Navy idea was more of a rogue fleet of swift attacks intended to disrupt enemy trade lines.

Since they weren't able to build effective battleships comparable to other seafaring nations (even Italy had better battleships at that time) they've mostly focused on fast cruisers and submarines. They're overlook air carriers role as well.

As for success - it wasn't effective for most of the WW2. Most notable kill by Soviet submarine was 'Wilhelm Gustlov' but it was only in 1945. As for battleships, top Soviet kills were only a few destroyers - across all fleets.