Will partially girdling a tree be enough to kill it?

Question:I have a sweet gum tree in my yard, and I was able to girdle it about 3/4 of the way around, and sprayed it with brush killer. The rest of the tree is against a chain link fence, and did not want to move fence to get chain saw in. Don't really want to carve the rest out by hand either though, but I want the tree to stop dropping "gumballs" in my yard. The tree is approximately 2-3 diameter.

Thanks,
Keith S.

Answers:
Yes I am pretty sure you have to go all the way around. Why not do this above the fence line. Better yet, why not just cut the thing down now. Felling a live tree is no more difficult than a dead one.