While the Smart Network Switching option is more to get you the best connection possible, it should, in theory help. If the wifi signal is weak or the internet connection behind the wifi signal is slow, it should automatically switch to mobile data. You would think that being out of range would trigger the weak signal situation, but no guarantees there.
Aside from toggling mobile data, how about toggling wifi as well? For years now, I've had a quick toggle or widget for wifi. When I leave a trusted wifi network, I turn my wifi off. Though I ran tests a long time ago and verified that android is actually really smart about conserving battery while still periodically scanning for a wifi network, I don't want to take a chance that my phone will connect to a network that I don't trust and I figure it has to be saving a tiny amount of battery life by not polling for open networks as I move around town. Just my own personal policy, but I'm wondering if toggling wifi off will force it to use mobile data instead. I'd think either one (wifi or data) should work, since it should poll for connections either way.