Fenix 5s notifications w/wi-fi

I just got a Fenix 5S non-sapphire w/o wi-fi. Coming from a wi-fi Apple Watch, I was able to see notifications from any area of the house because I was on the wi-fi network. While I love my 5S, I find that if I step away from my phone for just a short distance, I don't receive notifications. If I exchanged this for the 5S wi-fi version, would that improve? Would it pick up notifications from anywhere in the house, if it was on the same wi-fi network, or is it still going to be picking up solely on bluetooth range? TIA