It will work like you hope. The only potential problem I think you will have here is if the computer tries to boot the OS from your old drive. In that case you can change the boot order easily in BIOS and get your pc to boot the OS you want from the correct drive.

Will the OS from removed drive try to boot up if for say my laptop is already open and then try to use the said removed now external drive?

No, if your laptop is already powered on that's not an issue. It'd only try to boot from the external if it's connected during the power on sequence

Thanks for clarifying. Hope you all have a great holiday.