Only if Republican leadership has the courage to go right after Democrats on this issue with unmistakable campaign advertising. Otherwise voters are just going to think the GOP is doing their Me Too act, again.
This article says Republicans are planning to attack Demonicrats on trans tyranny support:
https://www.breitbart.com/politics/2023/09/18/transgenderism-tangles-texas-democrats-run-for-sen-cruz-senate-seat/