In the case that a gap remains between the convex and concave nuts after tightening, will this cause any problems?

No. There should be no problem when there is a gap between the convex and concave nuts. The concave nut controls the amount of torque regardless of the size of any gap. Even if all the HARDLOCK NUTS are tightened with the same torque, the gap will very from one set to another due to slightly different thread accuracy.