She said they could indeed do that, and within 24-48 hours they would ship out a drive that would get to me in 3-5 more business days, after which I'd send back mine. I asked if there was anything faster than that available. :-)
She ended up offering overnight shipping, which they'd normally charge for... but since they're having technical issues right now, they can't charge me, so it'll be free. She went and confirmed that the drives are in stock (presumably not in the same location she's in, but in their Texas fulfillment location) so it should actually ship today or tomorrow. I should have a replacement on Thursday. I have 30 days to return the old drive, or they'll "bill" me for it; she asked me for a credit card expiration date, but not the number. They'll ask me for that if they need it in 30 days. Huh.
My biggest gripe with Seagate right now is that their web site, on which I should be able to check the status of my return, doesn't work in Safari or Firefox. It insists I must use IE 5.5 or later, or Netscape 7.0 or later, to view a return status. *rolls eyes*
If this doesn't work, I'll ask Newegg for a replacement, or for a refund with which I can buy a faster, higher capacity, less expensive replacement... from them.