What you say is fine but it lacks details. Are you submerged or surfaced? How did you develop the speed and course information? This is all unclear. It is all vital.
Assuming you did develop accurate speed, bearing and course determination submerged, yes, you could fire based on bearing, provided you have properly set up your submarine position, entering the proper data into the TDC. Sure it's possible and the devil is in the details.
There are two different methods of using active sonar to do what you describe, WernerSobe's Sonar Only Targeting technique and my Dick O'Kane Sonar Only targeting technique. Both do what you describe.
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