Mid tier or not, if they even release a phone around $300 that can run x86 programs (my Intel Compute Stick reference) along with the mobile counterpart...it will get enough momentum for OEMs to start experimenting. 2GB RAM, 720P screen (cost savings), LTE w/ 16GB onboard storage (WIM Boot + mobile) plus expanded storage running on an x86 chipset does look achievable. Kinda best of both platforms (mobile/PC) for a cheaper price.
I'm not so certain that's possible at that price point. It will still effectively be running the full version of windows, with the full version of all applications. Users may be installing Norton, Free Downloader Pro, BitTorrent, and all sorts of applications that eat up CPU resources and don't have a proper efficiency mode. The Intel phones you are thinking of have only been made available with ported Linux and Android distros with erratic application support. A $300 Windows 10 Intel phone would have too many compromises to make it useful, especially when it will be expected to have Continuum. To be honest it's like the "Hololens will cost $600" mantra all over again.
Now to think of it, an Intel mid-range phone is pretty pointless if not outright stupid. An Intel Windows phone WILL be expected to run full Windows applications, ranging from Office to Photoshop to Crysis. That kind of necessitates it to be considered a top-of-the line phone, not a half-hearted experiment priced cheap so that people check it out. What logical reason is there to make an Intel phone that outperforms the 950 but then make whatever sacrifices needed to bring it down to $300? The Surface line is intended to be commonly sold, not an experiment. Spend the extra $200-300 needed for higher quality components and a decent battery.
I expect that if it does happen, The Intel Surface Phone will not launch for one or two years and will be considered a flagship much more powerful than the Lumia 950, and will have a year or two of Windows 10 updates and optimizations to make it feasible.