It might have negative effects if the web server itself can't reach the OCSP server. With the client observing the provided OCSP stapled response (or the lack thereof), it invalidates the connection. If the client would try to get the response itself, it would probably (unless configured otherwise) forgive the lack of response.
That happened to me earlier this summer when LE put all the OCSP servers into maintenance at the same time. One (or more) of my sites were, of course, effectively offline because there were no valid OCSP responses to verify my certificates.