Good idea. Seems to me that (depends on the individual ofc) straight PVEers can put themselves at a disadvantage for PVE. When everything is on-script no problem. When there's a goof up or things otherwise get off-script, and it's time to assess and act on the fly, I've seen them often freak out or just give up.
Since PVP trains more on quick, fluid, assessing and planning to fit the situation you'd be enhanced skill-wise. Not just knowing to wait for A cuz then it's time to do B and C. Also too you can be that guy in raids that instinctively runs strafes, and mouse-turns through NPCs making your self-rooting op mates wonder ***.
This made me remember the one time i healed a raid. It was 16m SM S&V. I was the only healer moving constantly and ****. All the others stayed planted (where they were supposed to be haha). Most definitely wasn't optimal but the PvP in me doesn't turn off lol