watchOS 5.1.1 later this week to fix the issue?
No. Apple will re-release 5.1 once they fix the issue.
I would rather wait for a fresh factory order than one in stock even if a replacement has WatchOS5.1 already installed. Just because some people upgraded successfully yesterday, doesn't mean that there aren't underlying issues in the current version of WatchOS5.1.
With a factory order, Apple should have resolved the issues with the OS by the time its built.
Apple will release 5.1.1 within the next week or so to fix the issues. It will require a brave person to be the first to risk their S4 upgrading to 5.1.1. when it arrives lol
A very, very similar scenario happened on the watchOS 3.1.1 update, but it took much longer for Apple to pull the faulty software. At that time, my Series 2 was just over a month old and it was bricked late at night. I opted for the express replacement through AppleCare+ and had a "new" watch the following day. That one came with 3.1 installed, and when they released 3.1.1 a few days later, I updated successfully. I never had any issues with that watch again (it sits on my bedside table now that I have a Series 4). I learned my lesson, never update within the first few days. Now I tell all my family members to hold off until I give them the go-ahead. To this day—nearly two years later—I still get that uneasy feeling in my gut when updating my watches.