Would an eviction be on a background check for section 8?

Yes, it will show up. When you apply for a voucher a complete background check is done on you and any evictions will probably show, especially when you must list each landlord you've had for the past three to five years. But you won't be denied a voucher just because you've had an eviction: each apartment complex or other landlord does its own background check and it decides whether to approve you based on their information. The housing authority can deny you a voucher if you were evicted from a public housing unit or if you were evicted while you had a voucher, inter alia.