I would say "no".
If anything, the BASIC might be considered the "command line" for the system, but not the OS itself.
If you step back to other system, such as the DEC PDP's. These, to, would essentially present itself as BASIC. You login, and you get the BASIC prompt.
But it's clear that in these scenarios, that BASIC is not the OS. The underlying RSTS or RSX were the actual OS, as those aspects managed the jobs, multiple users, etc.
Micros didn't need all that, they just needed routines to abstract the hardware.
The early systems were not very sophisticated, the line between the BASIC runtime and the "OS" (if any) was fuzzy indeed. Witness modern hobby BASICs that simply need the console driver routines for fundamental operation. I don't consider a serial port console driver an "OS".
But, consider something like the Atari systems. which has a built in extensible device manager that BASIC leveraged. BASIC was an add on for Ataris, coming in cartridge form. Now is a device manager an OS? Meh, "sorta".
BASIC on CP/M, clearly, DID run on top of an "OS" -- they ran on top of CP/M and it's BDOS services.
Finally, as we get in to MS-DOS, which was more and more like an OS (it did things like memory management, device abstraction, "TSRs", etc.) Offering more services than simple devices. Then the boundaries between OS and application program (including development and runtime environments like BASIC) were getting more clear.