No, Harvest doesn't have a way to automatically prevent your teammates from tracking time to a project that's met its budget. 

When your budget has been met, you can archive the project to prevent your team from tracking more time to it. You can still report on and invoice archived projects. For more information, see our article on archiving and deleting projects. 

You can also have your team switch to tracking to non-billable tasks once a project's budget has been met.