Certainly plausible. LBJ won that election, O'Daniel's enemies stole it from LBJ to keep O'Daniel out of Texas. If John Connally had not told the judges in South Texas to report their findings immediately, LBJ could have cheated in the South to offset O'Daniel's cheating in the West.
LBJ serves in the war per OTL. He had made that promise during the '41 campaign IOTL.
LBJ becomes Majority Leader after Barkely, meaning that the Fair Deal probably succeeds. LBJ saved the House from going Republican in '40, come '48 the Dems could have a larger majority.
So I could see UHC and Civil Rights in Truman's second term. If China doesn't intervene in Korea, a Dem (it could be Truman. Or it could not.) wins in '52. LBJ has a good chance of being on the ticket there or in '56 or '60.