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Yep. The customers browsers are going to throw a massive OMG THIS SITE IS HAXORING YOUR COMPUTER error. Same error if you try to use a self-signed cert, really a PITA honestly.
Only if they check the details of the error will they see its a URL mismatch, but how many users ever do that?
Your best bet is to switch your site to not use www, or buy the cert again with the correct url.