To extend this question, if the schedule can be the same will there be issues in a push/pull weld arrangement? The two materials are similar. The cold rolled is harder and may distort a little from the heating. The hot rolled is softer. Both are relatively easy to spot weld. The difference in their individual weld schedules is very small maybe 2%. Yes, they should run on the same weld schedule assuming similar thicknesses and compositions.
The question on push/pull is an issue of proper set up for push/pull not a question of hot rolled vs cold rolled. Proper matched cables and conductors, matching electrodes and positions are the most important factors. If any of these are not balanced, force or heat being generated will changed at one station and one weld will be out of balance with the other. All parameters that insure even flow and heat at the two stations takes precedence and is more critical than the material being welded.
Reference: RWMA Resistance Welding Manual 4th Edition
AWS C1.1 Recommended Practices for Resistance Welding