It wouldn't do.
As Jake said, typically those errors occur before XenForo code starts executing. So, yes, it is more likely to be related to Apache or PHP and therefore it is those error logs you should be interrogating.
However, could you clarify a little more about the issue?
How many users do you have awaiting approval?
Are you able to see the list of users, or does it not get that far? Or is it when you process the selected users. If the latter, have you tried Mike's suggestion of processing less users at a time? e.g. does it work if you, say, delete or approve only 2 or 3 users?
What add-ons do you have installed, and do any of them modify anything to do with users awaiting approval? Easiest way to check this is to add $config['enableListeners'] = false; to your config.php file and then try again.
Mike also mentions possible server restrictions. Does your server have anything like mod_security enabled? If so are there any related logs that contain any information about this error?