Yeah, that XFX PSU is a quality unit, and while even the highest end part can sometimes come out of the box bad, it's extremely unlikely with a Seasonic built unit, as all XFX PSUs are built by them.
Gigabytes specs do specify a 600w PSU, which is probably a good idea. That unit has a 45 amp rating though, which should be fine for that card as long as it's never pushed hard. If you plan to push it anywhere near it's limits, get a bigger supply for sure, but again, it would be a good idea. That should not cause any normal use issues though, of the type you are experiencing.
You should be fine on shipping. So long as it was post marked prior to the expiration they SHOULD honor it. I've seen the Egg pulling some sheisty shit lately though. They refused to even give me product specific information regarding several products they currently sell. They referred me to the OEMs who told me, "We don't know what Newegg has on their shelf or in their warehouse. They could have products they bought from us months ago.". Lot of help they both were. Anyhow, I think you'll be ok. Let's hope. When you get those parts back, if you have the same issue, I would immediately RMA or return the PSU and get a bigger one by XFX, Seasonic or another Tier 2b or above unit.
Tom's PSU Tier unit list:http://www.tomshardware.com/answers/id-1804779/power-supply-unit-tier-list.html
Don't be surprised if you need to refresh the page, any page, on Tom's, as there is a known issue occurring with the system.