Does the ezeio support WiFi?

For the ezeio, WiFi is just another way to connect to a network.
The ezeio does not have WiFi support built-in. You will need a WiFi Bridge. Basically a bridge is a reverse WiFi router.

A router connects to a physical network to allow wireless (WiFi) clients to connect to it.A bridge connects to a wireless network as a client and allows a wired client to connect to it.

The Vonets VAP11N is a low cost bridge that works well with the ezeio. It doesn't even need a separate power supply.

The bridge needs to be set up to connect to the WiFi network (SSID & password), and then you just connect the ezeio to the bridge as normal.

Technically, there is no functional difference between connecting through a WiFi bridge or a physical connection as far as the ezeio is concerned.

That said, WiFi comes with a major flaw. You need to set up the client (in this case the bridge) with the SSID and password for the WiFi network. Depending on who manages the WiFi network, there's a good chance the SSID and/or password will be changed at some point. The password then needs to be changed in all clients, or they will loose the connection.
..and the only way to change that password is to directly connect to the bridge - meaning you have to be on site.

So we do not recommend WiFi if it can be avoided.

Unless you own the WiFi network (router) yourself, eventually someone will change the password and your ezeio connection will fail until you can get to the site, figure out what happened, get the new password from the IT guy, pull out your laptop and change the configuration of the bridge.

For this reason, it's worth considering a cellular connection instead. The additional cost for the hardware and cellular service may be recovered in as little as a single site visit.