##Yes and No
Yes and No
You cannot write it so that the code picks up where it left off, after the fatal. However, you can use register_shutdown_function() to continue processing php after the fatal error.
I've written code that checks which kind of fatal error it was and then attempt to fix it before redirecting the user back to the same page, or dying.
register_shutdown_function is excellent for redirecting the user to a 500 error page with a contact form prevalued with the error info. This way I could have the users help me out by opening an issue on my github acct.