That was cool. But Lets just say the clock could indeed stay ticking on "other" machines.
Both of you guys are correct.
Windows and Macintosh classic used a "Cooperative Multitasking" meaning your background application (in this case the clock) may or may not keep running depending on how the foreground application was coded. The programmer was responsible for surrendering the CPU.
The best example I can give is that I had a poorly coded windows 3X artillery desktop game. After setting the trajectory and power, when you pressed fire, the game would lock out background tasks until the cannon ball stopped. That really sucked if your background task was a xmodem BBS transfer or a sound player.