User blog comment:FairyRaven/Fairy Tail Chapter 336: In Order to Live Today to the Fullest, Review and Commentary/@comment-77.195.192.240-20130624072334/@comment-7418318-20130624085458

It's already established that any changes in the present didn't affect the people who traveled back in time (F-Lucy still remembered being captured, even after she helped P-Lucy to avoid that capture and F-Rogue still remembers that not a single Dragon came through Eclipse in, despite the seven Dragons being in the present right now to give to examples).

If destroying the Eclipse Gate now suddenly makes all the timetravelers disappear it would change the fundamental laws about time travel that were so far established in the manga.

I guess theoretically it's possible that the Eclipse Gate contains magic that prevents any such cascade effect, but since it was created to change the present by changing the past such protection would defeat the very reason it was build in the first place.