You have two different questions, one in your subject line and one in your text body:
Can Git be used to transfer large (6+ GB) files across a network link?
Yes, it can.
Wondering if GIT is a good option to accomplish this
No, this is definitely not a good option. Its badness is somewhere between "somewhat bad" and "terrible", depending on how reliable your link is. If your link is extremely reliable, this is merely a somewhat-bad option. If your link is pretty unreliable, this is a terrible option, because Git transfers do not restart partway through. A commit either gets all the way across, or Git starts over from scratch.
Using rsync will enable you to transfer large files with restart. See https://unix.stackexchange.com/questions/48298/can-rsync-resume-after-being-interrupted.