If you've still got 4 shifter positions on the column linkage, you'll have reverse, but it might not be in the traditional position in the "H" pattern. I think that swapping side covers is going to be a bad idea if it changes the shift pattern. The rear linkage is the reverse/1st. gear shifter, and if the direction the bellcrank is pointing is different, the location of 1st. and reverse will be swapped.
Jerry