I believe Haines can and will wrestle under the new RS rules. I believe whether he will or won't at NCAAs depends almost entirely on his will and whether the coaches think it's in his and the team's mutual best overall interest.
I firmly believe Levi controls his own freedom, so he doesn't need to be freed.
Statistically speaking, this is not obvious to me. Kyle Dake is a four-timer who wrestled as a true freshman without a gray shirt or taking any RS. Cael and Logan both redshirted their true freshman year.
We may add Spencer and Yianni to the Cael-Logan grouping at the end of the year, albeit with injury and Covid year asterisks. But absent injury and Covid, Spencer and Yianni very well could've been added to the Kyle Dake grouping of non-RS/Gray shirt/Olympic RS four-timers. Additionally, Pat Smith, the first four-tiner, didn't wrestle in 1993 (his true Senior year), because he took his RS during an Ok St NCAA sanction year rather than a free transfer to ASU. Otherwise Pat Smith too could've been added to the Kyle Dake grouping.
So, percentage-wise of wrestlers who wrestled four years and either started as a true freshman without gray shirting or true RS freshman wrestlers (with or without gray shirting), I doubt the statistics point to taking a red shirt as an obvious advantage to becoming a four-time NCAA D1 wrestling champion.
I believe other factors, some beyond one's control (e.g., competition in the weight class, injury, wrestling thru injury, stylistic challenges, weight cutting approach, and differences in nutrition and recovery approach), could very well have as much if not more statistical significance.
Dare I say, it may even take a near "generational talent" to achieve the feat. It's probably too early to hail Levi as such.