If the certificate is there, then chances are that it is used for something, and that something will probably break when the certificate expires.
In your case, if you use pure NTLM, then it seems that no certificate is used at all, so maybe you can let the certificate die and see that nothing happens. However, authentication in SharePoint can be complex so I won't claim to give any definite guarantee here.
Note, though, that the NTLM protocol is vulnerable to offline dictionary attacks: someone observing the traffic won't see the passwords "as is", but will learn enough to "try passwords at home" at a rate limited only by the number of PC that the attacker can muster -- and that will be counted in dozens of millions per second. Not many user-chosen passwords last long under these conditions. And, of course, a HTTP-only site is easy prey to attackers: if you use authentication, then you fear unauthorized accesses; if the data is confidential then a passive eavesdropper will see the data as it is retrieved by normal users; and an active attacker can hijack connections at will (that's the classic Man-in-the-Middle: the attacker forwards bytes in both direction, and when the authentication has been done, he takes control of the connection).
In simple words: if you really need some security in your case, then it seems highly implausible that you can get away with not using SSL. And if you do not need some security, then why are use using authentication at all ?