No, it will not. Google Apps provides you with many MX servers for redundancy in the event of a problem. MX records have a server for sending attempts to send mail and its priority (IE, which server are you on the queue to receive mail for this domain, if the other is not available). You could not add the server with the lowest priority to your DNS. Typically, the mail server does not try to connect to it (aspmx5.googlemail.com), unless all the others were available. In this case, we will probably have problems to worry about :)
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