A steady current itself doesn't effect the ships helm or course, both are moving in the same water
and the ship doesn't "see" the current
Only when you hit the boundary line between two differently moving flows such as when you go through a strong eddy line, or if the current is different at the lower portion of the hull from the surface does the vessel get knocked of course.
does effect it however in the way you describe, depending on where the bulk of the windage is in relation to the underwater dynamic center of lateral resistance (pivot point). This is most noticeable when you go astern. the pivot point moves aft and the windage blows the bow off downwind so you end up reversing into the wind
on most yachts and some ships.
The same effect is a part of the reason why yachts develop weather
helm (want to turn into the wind) as they move faster, but this is also caused by the hull shape changing and the force from the sails
moving off to the leeward side as the boat heels over.
Sounds like an interesting project
, all the best with it.