Only those with MARSHA access and even they would have to know how and specifically look. Its far, FAR, from being across the board at all properties and even then your front desk worker at 1am is unlikely to know how to do so unless they've been there a while and actually have access.

In general they have no reason to look nor care where else you might be booked. They're just as overworked as the rest of us and have little time to nose around. Many of them at wearing 15 different hats at this point(house keeping, night audit, front desk, security, insane demand meeter, etc...)

MARSHA is an old as dirt command line system that even most elite agents and their managers don't have access to because marriott in their infinite wisdom doesn't think they need it. Its not user friendly at all and isn't something thats remotely simple to learn. So the people that have access and know how to use it are few and far in between.