Yes it is possible.
Set up a field for selecting the payment options e.g. radio buttons.
Set up two choices - Cash and Paypal.
Set up two logic rules for the "cash" option.
Something like if Radio-button = "cash" then skip to end and submit form and a second logic rule, if Radio-button = "cash" then send email notification to user (auto-reply) and to Admin (submission notification)
For the Paypal option, if you choose that the form should proceed as normal and direct to paypal for payment and back to the merchant site and will send the usual email notifications to the Admin and to the user.