According to this article, they got the approval to bypass the limits on February 14th.
https://www.usatoday.com/story/news/factcheck/2021/02/25/fact-check-ercot-not-gov-abbott-sought-bypass-emission-limits/6803971002/
Though the inclement weather before February 14th might have resulted in deaths, the need for higher emissions didn't become apparent until February 13th. The day after, that was requested and approved.
That did save lives. Just not all of them.
https://en.wikipedia.org/wiki/February_13%E2%80%9317,_2021_North_American_winter_storm
Apologies for using Wikipedia, but I needed a timeline of when the storm began. If you have another source, I'll be happy to consider it's relevance.
In either case, the storm killed them. Not the EPA executive order.