New purchaser of Adobe Photoshop elements 15

There is not a subscription for PSE15, no.

A small amount of internet is needed to convert the redemption code to a serial number, once, and to license the software on up to two computers once you have the serial number, then periodically the license is checked, I imagine. These activities wouldn’t use much data, I don’t think.

There might be some internet content that PSE tries to retrieve from time to time. If your internet is charged by the megabyte that might be a concern. If you just pay a monthly fee no matter how much you use then it’s probably ok.

The internet would be needed to update to PSE15.1 at some point, and to get any Camera Raw plug-in updates if you have a new camera that’s come out after PSE15 was released, until mid-summer when PSE16 would likely be programmed and they stop CR updates for PSE15. Updates would be several hundred megabytes in size. If you can get by without updating or if the internet is fast from time to time or you can take your computer somewhere else with faster internet periodically for updates that you should be ok.