Commerce 2: Can Cash and Check payments be implemented?
You can do this by adding an additional payment gateway.


Add a role, Pay with Cash or whatever you want to call it.
Add a new payment gateway (at /admin/commerce/config/payment-gateways/add). 


Name: Cash or Check
Plugin: Manual
Customer: Limit by Role: Pay with Cash role



The "Manual" gateway does not ask for any payment information, so orders with the manual payment selected (which only users with the Pay with Cash role will be able to select) will automatically be processed as completed when this payment method is selected.

If you want to record bank info for checks, you can make two separate gateways, one cash and one checks, and then customize the check gateway with additional fields.