Your question: "If an existing GSA Contract under 621i was awarded to a contractor under NAICS Code 561320 can a Task Order be awarded off of that contract with a different NAICS Code than 561320?"

Bottom line answer: In short, yes, however any set-aside decision must assess all vendors using the $30 million value established by the SBA for NAICS 561320, irrespective of any vendor's actual NAICS registration(s) in sam.gov (which may correlate to a higher or lower dollar amount recognized by other basic contracts where a different NAICS is selected).

For purposes of issuing orders under a GSA scheduled contract, a primary use of the North American Industry Classification System (NAICS) code is to determine the small business set-asides IAW FAR Subpart 19 and VAAR Subpart 819.5. 

Use NAICS 561320 to determine the size standard for ANY ORDERS under GSA Schedule 621 I, and refer to Department of Veterans Affairs contracting guidance promulgated at https://www.va.gov/opal/nac/fss/schedule621i.asp

Refer to the GSA Schedule 621 I solicitation and vendor-specific contracts if you have specific questions about award procedures.