Distressingly likely. It's easy to overlook the fact that Microsoft had considerable dominance in BASIC implementations even before the IBM PC took off, with several major vendors shipping a rebranded version of Microsoft BASIC in ROM (Commodore BASIC, Tandy TRS/Color BASIC, Applesoft BASIC), and others selling it as an add-on package (e.g. Atari Microsoft BASIC). They probably would have gotten a foothold operating systems one way or another once multitasking became a big deal.
On Thomson computers also, it was "BASIC MICROSOFT 1.0" as standard 'OS', provided as cartridge on TO7 and included as ROM on MO5 (and later, on TO8), if I am not mistaken.
