Can phone app connect with car over wifi?

[Nagarjuna]

Friends, bear with me, I am still a week away from getting my Model 3.
I live in the wilderness: no LTE signal reaches my house, no LTE signal reaches the garage. But I have very good wifi covering both house and garage; my phone, too, gets its phone signal + net connection from the wifi.
Q: Can I wake up and control the car only over a LTE (as the manual seems to say), or is it possible to reach it over our local wifi, too?
Kindly advise!

 

[907tracer]

I just turned off data on my phone and the app did control my car still. I still have the premium connectivity but I am pretty sure it's connected over wifi.