So it doesn't check if you can actually host it (because it can't check, there is no other way than checking on your actual network)
Literally all it does:
if org belonging to ip contains wireless, mobile, cellular, verizon, at&t, t-mobile, sprint: IP is cellular (really bad way to determine if an IP is cellular or not by the way)
if IP belongs to asns 701, 6167, 22394, 21928, 23402: IP is cellular
if IP belongs to asns 7018, 20001: IP is not cellular
if none of above if statements match: IP is not cellular
if IP is cellular: no you can't
if IP isn't cellular: yes you can
That's it, that's the entire site.
And saying "Public-looking IP" doesn't make sense, you'll never get anything other than a public IP from icanhazip (or any other ip fetching service). Also having a cellular IP doesn't automatically mean you are unable to receive inbound traffic, some providers sell "mobile broadband" that allow you to open ports, etc.
