The short answer is no. We built a system that allows you to use https and http.
For http only shops, we automatically create a sub-domain name for you which looks like this: xxxxx.firepush.io .
The main drawback here is that your user will see only this subdomain name and not your site domain name. This also means that you will not be able to export your subscribers should you choose to leave Firepush.
Without https, you also won’t be able to use auto prompt message which collects up to 30% of subscribers.
Alll shopufy shops can activate SSL certificate, if you have not done it yet go here https://help.shopify.com/manual/domains/ssl and check how to do that.