Is NRTL approval required for the sub components I purchase and assemble into a final product in order to sell the product in USA?
For safety approval in the USA all parts of your system that connect to AC power mains will need to be component certified and labeled as such from the manufacturer. This will also apply to any components connected into any circuits with high voltages connected to the same circuits. I recall that the threshold for "high voltage" is anything over 48 volts.

If any of these components is not safety approved you may elect to pay extra fees to the certification lab to test and validate those components. (Note that this adds more weeks to the time to get your product tested). Also note that the testing is often destructive and you may get your system back with the components in pieces or cut open. The lab may actually ask you to submit additional components for testing and inspections. 

Then whenever any part of your system includes parts that are AC mains connected, connected to "high voltage" or have any types of moving parts considered to be potentially dangerous then you will have to submit your system to the lab for testing and validation as well. Moving parts could include things such as fans, motors, solenoids, sliding parts, or even hinged parts. It is generally required that multiple systems be submitted for such testing. Once again one or more of the systems may come back in an inoperable state or in pieces. 

There are also several types of safety approval listings that you should learn about which involve things such as how you source the labels that show the approval and if the factory needs to be inspected for each production run or on a periodic basis. The part of the factory visits is to ensure that the equipment is still being built in the originally certified configuration and that necessary tests are being run with inspected and calibrated test gear. Such tests may include hipot testing (high potential tests).