Hm. Let me tell you how I see the whole would-be course of events.
They will not start building the whole thing from the tunnel for starters. They have to build railroad through Yakutia's tundra and Chukotka mountains first. 3500 kilometer 'stretch', as they point it in articles. Single railroad stretch through 3500 km of tundra and mountains, 10-month winter and 2 meter snow coverage, permafrost, coldest of 'inhabited' places on Earth (-68 deg. C., how do you like it?). It's like second BAM, but it would be ten folds troublesome as BAM is/was. There will be no cities in places like that, just small service stations. Noone will want to live there, and still you'll have to maintain 3500 kilometers of snowy/rocky hell. Maintenance cost alone will eat this railroad from inside. There's still no railroad between Kamchatka and mainland. There's no roads on Chukotka at all, save winter roads (wheel-pressed snow). There is an automobile road between Yakutsk and Magadan, the infamous Kolyma highway, it's just a dirt-track, and it's still not connected with main transportation network that is far away at south. Why is it, how do you think? Because it's not worth it. And all these projects about Bering strait tunnel is just some idle talks.