Israel is sanctioned internationally. They play at the lower levels of the IIHF championships regularly - every year since 1992. They have had a U18 team since 2001. The Israel Ice Hockey Federation exists. The Canada Center in Metulla is a full-sized ice rink.
With the players mentioned above - Tanus is ineligible for a whole host of reasons, Birbraer is 40 years old, and Kozhevnikov (also nearly 40) and Sherbatov already suit up regularly for Israel. Levin is probably eligible, but most of the rest of the team is made up of Israel league amateurs. They wouldn't even be a mediocre D1B team; they'd be an elevator D1B/D2A team at best. Most likely a solid D2A team with their best possible roster.
I'm not saying that they'll be competing with the likes of Canada anytime soon, but they definitely have a hockey program.