With some very rare exceptions, the answer is no, you need the BT link to the phone in order to access the internet.
The Edge x30 can access the internet over WiFi as long as you are not recording an activity. Once the activity is recording then you must have BT to access the internet.
Watches with WiFi and LTE can only use those connection types for bulk download/sync type activities. To save battery those connections are disabled until a specific sync delegate is called then turned off once the bulk download is finished. They generally are not available for general http requests. You could probably work out something, with the sync delegate, but you will have to wait for wifi to connect every time before you can access the web request.
On top of that wifi is really hard on the battery, so you really wouldn't even want to keep trying to connect on a regular basis.
I think LTE is connected more of the time than wifi, as it allows the watch to get texts, etc, but not sure, as it's only in the US and only with one cell provider, so I've not heard much about how it works.
