From what I have found there are three ways to print an envelope from a Neos generated template; however, all three are not ideal.
Create a template with a second page formatted as an envelope. Once the document is generated, open in Word. Print the first page in regular letter format and then print the second page in envelope format. It appears the tray settings from the template are lost in Word Online.
Generate a template, "Open in Desktop App" to get the Mailings tab to print an envelope,
Create an envelope template to generate,the downside of this is that the case will end up with mayenvelopes saved to the case docs tab.