CUIC should be already sync'd to UCCX. UCCX gathers account information from CUCM via AXL. If CUCM is sync'd to AD via LDAP, then you should be able to retrieve and authenticate domain accounts with AD. Did you purchase an CUIC Premium license from Cisco?
Are you talking about agent finesse logins or administration logins to UCCX?
CUIC and UCCX are two different things.
Typically, in most environments, you'll have ldap sync on CUCM and those users will be enabled for UCCX.
I had the same exact question and I had read the document that Mark (in this thread) provided. But I had several questions about the standalone and opened a TAC case. The doc that Mark provided, Cisco does not state that some of the items only applies to UCCE version with standalone CUIC .
Here is the response from TAC on the LDAP and users for the UCCX version of standalone CUIC.
here is my question (Q4) and his answer (A4):