As far as software goes, sure. IBM, at least, has put a LOT of effort into maintaining upward compatibility. There's business logic that's still happily being used by a lot of large organizations.
As far as hardware goes, probably not:
- The older systems are slow, and consume a lot of power, and consume a lot of air conditioning (or water cooling). A newer system of equivalent power costs much less to run; the hardware replacement costs are dwarfed by the power/cooling/space that's not used by the replacement.
- There aren't many parts available for the older systems. Even when there are spares, it's going to be less expensive to replace an older system than fix it. The older the system is, the truer this is.
- There are few people left to fix the older systems. The manufacturers (e.g., IBM) don't maintain them any more, and I doubt anybody's even offering training in how to maintain/repair the older systems.
Economically, it doesn't make sense to run hardware that's that old. Replacing it with newer (but software-compatible) hardware costs less, and gives you a system that's more reliable and more maintainable.
However, economically, it does make sense to run software that's that old, if the business logic is still valid. (But that's a whole other conversation.) So, yes, there are an awful lot of business still running software that was written that far back.