The way Albert Speer described it in Inside the Third Reich ,SS membership didn't grant extra influence to those who'd made their careers outside it, but rather was a way for Himmler to extend his influence. p369-370:

Himmler had conferred an honorary rank in the SS upon almost every government minister whose personal or political weight he had to reckon with. He had reserved a particularly high distinction for me; he wanted to make me an SS Oberstgruppenführer, a rank corresponding to that of a full general in the army and one very rarely conferred. But although he let me know how unusual the honor was, I refused his offer with polite phrases.

[...]

By conferring such ranks Himmler of course meant to gain influence and thrust his way into areas not yet under his command. My suspicions proved only too justified: Himmler promptly made every effort to push his way into the field of armaments production. He readily offered countless prisoners and as early as 1942 began placing pressure on a number of my assistants. As far as we could make out, he wanted to turn the concentration camps into large modern factories, especially for armaments, with the SS continuing to have direct control of them.

The recruitment attempts were verified by Gitta Sereny in Albert Speer: His Battle with Truth , where she accounts for several letters between Himmler and SS staff showing he was preparing the paperwork to enroll Speer in 1942. And likely behind his back, since the SS staff were ordered not to contact Speer directly in the matter.

She also makes the case that if he actually had had SS membership, Speer may have gotten the death sentence at Nuremburg.