It depends a lot on how you define productivity. If it's heads down hours, sure.
But on the flip side, here's some things from my experience that I would count as productive:
- saw someone looking angry at their computer for several days. Asked them what was going on. After a chat realized his project was never going to work so we canceled it. It would have taken weeks/months for us to realize this if I didn't see him physically boiling at the desk.
- need a quick chat with Bob and Alice. Saw they are at their desk, just rolled over and had the chat because they happened to be there. Vs trying to find time on calendar, ending up weeks later.
- crown jewel: ran into a dude I used to work with, now in a different department. Turns out he's working on something similar to me. That started a bunch of conversations, ended up combining efforts and building platform. Now running essentially 3 businesses based on 1 tech investment. Wouldn't have happened if I didn't bump into him in the elevator.