First, I apologize for the delay in answering.
You got it absolutely correct. The experimental aircraft, an XC-123A was America's first jet transport, flying first on April 21, 1951. One Boeing B-47 jet pod containing two turbojet engines was carried under each wing. Testing revealed an on-wing leading edge location was better for tactical operations. So, production versions of the C-123 were piston-powered.
The US Air Force did use auxiliary jet engines on modified C-123s for Arctic operations. Further experiments in 1966 and 1967 showed the value of similar-placement of similar auxiliaries on C-123s in the Vietnam Conflict (our US congress never did declare war on Vietnam so officially it was the Korean Conflict). I served in US Naval Aviation at that time. (Am 88 years old now as of last month).