Tag Max Time with Change Script

If I have a tag whose max sample time is set to 24 hours, but this tag also has a tag change script, will the script fire at the 24 hour interval? I had not thought about this when configuring a tag and think it may be a source of some issues with my project.

Only if the value at that point in time is different from the last OPC value.

script value change will trigger each time the value change, if your tag changed 50 times in 24hours it will execute 50 times.
If your are talking about performance issues well the script will execute at the server not the project itself, it actually depends of the complexity of the script and the specs of the server.