Yes, but computing Heegaard Floer invariants is still not very efficient. I'm not sure about knot genus calculations, but tables of isotopy classes of knots were computed up to 16 crossings using classical methods. My understanding is that the algorithms for Heegaard Floer computations are not computationally practical for that number of crossings. Thus the fact that they detect the unknot (much weaker than separating isotopy classes) adds nothing computational to the picture.