We don't actually know a ton about how Morgoth's recruitment process worked, so it's hard to say with certainty that it was the only reason Sauron joined him1. However, Sauron's love of efficiency was certainly a major factor; in an essay titled "Notes on Motives", Tolkien writes:
[I]t had been [Sauron's] virtue (and therefore also the cause of his fall, and of his relapse) that he loved order and coordination, and disliked all confusion and wasteful friction. (It was the apparent will and power of Melkor to affect his designs quickly and masterfully that had first attracted Sauron to him.)
History of Middle-earth X Morgoth's Ring Part 5: "Myths Transformed" Chapter VII "Notes on motives in the Silmarillion"
Of course, going along with Morgoth would have required a few other commitments, most notably:
- Hatred of the Elves, and their allies
- Hatred of the Valar
It's not entirely clear to what extent these applied to Sauron before his fall; he certainly came to hate the Elves, and developed a healthy mistrust of the Valar, but maybe Morgoth just had really good training videos. Again, we don't know.
The published Silmarillion does make the following observation about Morgoth, and his recruitment:
Understanding he turned to subtlety in perverting to his own will all that he would use, until he became a liar without shame.
The Silmarillion II Valaquenta "Of the Enemies"
So it's possible that Morgoth made Sauron certain "promises", though whether or not he did (or, if he did, what he may have promised) is unknown. If he did, they may have resembled the promises made to Ossë, in Melkor's (ultimately unsuccessful) attempt to gain his allegiance:
Melkor hated the Sea, for he could not subdue it. It is said that in the making of Arda he endeavoured to draw Ossë to his allegiance, promising to him all the realm and power of Ulmo, if he would serve him.
The Silmarillion II Valaquenta "Of the Maiar"
The published Silmarillion also notes that Sauron had grown rather fond of his high status in Morgoth's army:
Sauron was ashamed, and he was unwilling to return [to Valinor] in humiliation and to receive from the Valar a sentence, it might be, of long servitude in proof of his good faith; for under Morgoth his power had been great.
The Silmarillion V *Of the Rings of Power and the Third Age"
So we can presumably add "advancement opportunities" to the list of things Sauron liked about Morgoth, Inc.
1 Maybe Morgoth offered great dental benefits, or had a good 401(k) program; we don't know.