No, he did not. He bought "Q-DOS" (what became MS-DOS) from a company called Seattle Computer Products when IBM came calling to license Microsoft BASIC, then the hot programming language for microcomputers. They mentioned they were also in the market for an OS, and would be talking to Digital Research, which then practically owned the OS market for micros with its CP/M. The rest is history. Bill Gates snagged the OS business by buying a CP/M knockoff and offering to IBM. He became the world's richest man, and Gary Kildall, who wrote CP/M and headed Digital Research, died at a relatively young age, probably from thinking too much about the day he allegedly pushed off the IBM meeting to meet with Atari instead.
CP/M-86 was in fact offered by IBM on the original IBM PC, but Gates' offering was the one that got the IBM-DOS moniker and became the standard.
Digital Research attempted a comeback with DR-DOS, a "better" DOS, but they'd lost market momentum and basically went down the tube. DR-DOS is owned today by The SCO Group. I don't know if they still offer it or support it as a product.