My name is Aaron, I'm a guru here at Shopify!
Absolutely! That's possible using custom payment methods. The first step is to create a manual payment using the guide right over here. What you can do there is create an 'invoice me' option, to allow your customers to place orders without remitting payment right away.
Then, you can create an invoice from within your admin using draft orders - the guide on that is right over here! Once created, you can then email this invoice to your customer.
Hope that's helped! Please feel free to give us a call or start a live chat at any time, we're open 24/7 for your convenience and always happy to assist!
Aaron | Shopify Guru