cathaychris welcome to Flyertalk and especially to the QR forum.
The visa will be sent to you via e-mail.
If, as you state, you have provided no e-mail address how can the Immigration authorities notify you if the visa is granted or not. It cannot even contact you to tell you that the application is denied because of missing information. According to
https://qatarairways.zendesk.com/hc/...py-of-my-visa- you need to produce a copy of the visa in DOH. But this appears to have been superseded by an online system.
However it would appear that they have obtained an e-mail address from your QR booking so it may not be a problem.