Yes, having a cloned machine will cause problems with both SCCM and (WSUS) updating. The issue with duplicate client UUID/GUIDS is discussed in this technet blog here.
Because this is generated at install time, you should not clone a machine with an SCCM client installed, so uninstall it before cloning, and install it on the clone after completing a sysprep. (sysprep /genealize /oobe /reboot
is usually what you want).
Likewise, you shouldn't clone a machine that's domain-joined, as this can cause problems with Active Directory. After your clone target is disjoined from the domain and the SCCM client is uninstalled, you should be able to clone it safely (though some 3rd party software doesn't handle cloning well either, so check with your vendors). Once the clone has finished, sysprep the source machine, then put it back on the domain and reinstall the SCCM client.
That sequence will properly create distinct the GUID, UUID and SID values, which will prevent the problems that arise from having [improperly] cloned machines in the same SCCM hierarchy or Active Directory domain.