I submitted my Sprint phone replacement order at 11:00a CST on 01/19, got the confirmation email at 11:05a CST on 01/19, and received the UPS package at 10:55a CST on 01/20. In less than 24 hours Sprint got me a new Touch Pro with an additional battery.
I did not get any follow-up email indicating the phone had shipped. Before I received the package this morning I sent ecare an email requesting the latest status, to which I have not yet received any reply - but at this point I don't think it matters!
Thank you Orionsbuckle, these forums rock.