Will the credit pull affect my applicant's credit score?

No. The Intellirent TransUnion credit reports are a soft pull.

Our direct partnership with TransUnion provides an integrated identity verification (IDV) questionnaire that needs to be completed by the applicant with the social security number. 

The applicant is verifying their identity through this integrated IDV step. Passing the IDV is a  request from the applicant directly to TransUnion asking that their credit reports be released.

See also, 

What is the TransUnion Identity Verification (IDV)?  

 You can also check out TransUnion's help center here for more information on their reports.