Tony has it right, you can dequeue the style without the site having an error. That is because of the way CSS works. If the DOM can’t find a specific CSS class/ID that is in the HTML it is simply ignored. Tony is also right, that you may need to add some styles back in if they were included in the, now removed, CSS file.
If you were removing a JavaScript file on the other hand you would need to be more careful to make sure that one of the removed functions wasn’t going to cause a conflict elsewhere. A quality theme developer will take that into consideration and often wrap functions to make sure all functions are there, but that’s not always the case.