CAP is not an air carrier, so no, it would not interfere with FAR117. Not even commercial flight instruction interferes with FAR 117, provided it is not being done for an air carrier.
§117.23 Cumulative limitations.
(a) The limitations of this section include all flying by flightcrew members on behalf of any certificate holder or 91K Program Manager during the applicable periods.
117.3
Certificate holder means a person who holds or is required to hold an air carrier certificate or operating certificate issued under part 119 of this chapter.
Having said that, many air carriers still have stricter policies than FAR117, so best to refer them.