Not really -- the DPS'ers damage per second will be the same. Their total damage will be lower since the healers end the fight sooner. E.g. DPS player does 300 DPS for 40 seconds instead of 60 seconds. Same damage per second but shorter fight time, so 12k damage instead of 18k.

The only caveat is that the exact time of the fight can be influenced by the DPSer's buff timing, so if the fight is shorter and BFB/Raging Strikes would have otherwise been up, then the shift could reduce their DPS.

The only other exception is if the fight has high and low periods of DPS for a class (like T4 for BLMs). For example, BLMs do high DPS during p1/4 on T4. If healers DPS during P2/3/5/6, then those "low DPS" segments of the fight (for the BLM) will be reduced, and the high DPS segments will be inflated, spiking the BLM parse.

If healers only DPS during p1/4 with lolol Holy, then the BLM parse will actually be reduced because less of the fight exists during high DPS periods.