No, a change in pushrod length won't be necessary. Going with different ratio rocker arms, if that's all that's changed, doesn't effect the pushrod length. However, your valve springs become an area of concern.
Going from 1.5 RRs (which in actuality would probably be in the 1.4x area) to 1.6 RRs (which will be much closer to 1.6 RRs) will cause about .030" valve lift.
What that does is cause the valve springs to compress more by about the same amount. Since most stock valve springs are pretty close to being maxxed out on how much lift that can safely handle, the 1.6s can push them over the limit.
It's best to go with better springs when moving to 1.6RRs from 1.5s, especially if the performance increase you'd expect can be realized as the top of the RPM range.
Just my thoughts.
Jake