Short answer: Generally no. Participation is measured among benefits-eligible (usually full-time) employees, so part-timers who aren’t eligible for the plan are typically excluded from the calculation.
Carriers calculate participation on the pool of benefits-eligible employees; normally those working 30+ hours per week. Part-time employees who aren’t eligible for coverage usually drop out of both the numerator and the denominator, so they don’t help or hurt the participation percentage. Exact treatment varies by carrier and state, so confirm how a given carrier counts part-time and waived employees.
Sources
Take Command, Minimum participation rate requirements for group health insurancetakecommandhealth.com/blog/minimum-participation-rate-requirements-for-group-health-insuranceeHealth, Group health insurance requirements and eligibilityehealthinsurance.com/resources/small-business/who-is-eligible-for-group-health-insurance