Interesting question, and based on what I found at https://www.vintagerockmag.com/2022/05/story-of-the-song-hey-baby/ you are correct: 
Armed with Hey! Baby, Dream Girl and a couple of other collaborative efforts, Channel took the songs to Major Bill Smith who owned a studio in Fort Worth, premiering them on guitar at Smith’s home. The following week, Channel was ensconced in Clifford Herring Studios where he met Delbert McClinton and his band, The Straitjackets. McClinton ended up collaborating on Hey! Baby with memorable results, picking up the harmonica on its second take. although Channel wryly remarked: “Nobody told him to do it.” The session’s musical director, Marvin Montgomery, also thought that the tune needed an additional instrument, duly providing piano on the third and final take.  

Channel would also agree with you regarding its contribution to the song's success. From the same article:
Upon his arrival home, Channel was informed that he’d be performing some concerts in England, but McClinton would have to stay behind. It didn’t go down well with Channel who told Smith: “I’m not going to England without Delbert – his sound is half the record.”  

I read that also.  Sounds like Delbert had an influence, whether intentionally or not, on a number of hits.