How create a product form without actual payment?

We're trying to take preorders for a school fundraiser. Is there a way to disable the payment function on the form, so that just items selected will be submitted to the email recipient?

Yes that is possible by using "Purchase Order" Payment Integration. 

Check it out here on how to create one https://www.jotform.com/help/460-How-to-Create-Payment-Form-with-Purchase-Order

Let us know if you need further help.