All Macs come with free software (iMovie, iPhoto, Garage Band, iWork suite, basic email, web, chat apps, etc.) that you can use with no problem regardless of what Apple ID is signed in.
If a paid application from the App Store is installed, the current installed version will keep working even if you sign in with a different Apple ID. For example, Final Cut or Logic. However: if you attempt to update the software via the App Store, it will ask for the login of the account that installed it- that is the account of whoever you bought the Mac from and most anyone will have deleted their login info off the machine before selling it.
So basically, my understanding is you'll have a working current version of paid app-store apps, but with no ability to update them unless you purchase the app with your own Apple ID. (Or have access/permission to use the purchasing Apple ID).
Third party/non-App Store software like Office, Adobe CC, I have corporate accounts for so I've never worried about them being unregistered, but I *think* third party paid software also will keep working. It might even update no problem so long as the serial/user information remains intact. Unless it's on a monthly/annual subscription in which case you'll need those credentials at whatever subscription renewal intervals.
To my knowledge Mac software is never tied to a hardware ID of the machine, but it is tied to Apple ID or third party serial number/user account registration.
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