On the one had running is a life long activity for some, and running with family members great bonding, but depending upon the kid, I agree with Dunno about the risk of injury/impact overuse - especially in higher level girls and girls once they hit puberty (lots of girls at risk for patellofemoral syndrome, etc, and the flexibility that makes some girls good at gym may mean their running stride risks their knees...).
DD already has some knee pain off and on with 20 hours a week - and I trashed my knees between dancing and running - probably depends upon the kid, their hours and their build - and I would expect most gymnasts to be fairly "good" at running distance at least due to their fitness level and natural ability to push through things....
I'd be much less worried about boys due to their natural build...