dwls and probable search

Yes, as long as he had probable cause for the initial stop he is entitled to search whether he charges the first offense.

A police officer needs "reasonable suspicion" to detain you. In your case, the license plate violation was their reason to stop (detain) you. They can detain you for a reasonable period of time while they investigate the reason for the stop. I assume they approached and asked for your license and registration. If they detected signs of alcohol ingestion, that gives them a new reason to detain and investigate possible DUI.

From there, they need probable cause to search - in your case, to search for the source of intoxication. They can search anywhere in the passenger compartment that substance is likely to be found. If they found stolen property as a result of that search, it may be admissible.

I say "may be" admissible because if they are searching for alcohol, but then start rooting through your stuff, they may have exceeded the scope of the search. You don't mention what the property is they found.

The fact they didn't arrest or cite for DWI isn't the issue. Discuss the search issue with your attorney.