When in that screen, yes. Otherwise, unlikely.
The Wifi chipset in an iPhone is always doing something. Forget just being on that settings screen, Wifi is doing things when the iPhone is locked, disconnected from wifi and the processor is asleep. It does this by using its low powered chipset very efficiently with instructions passed to it by the processor before it goes to sleep.
So for example, the iPhone is always scanning local BSSID's data to cache for later use....
So if I disconnect the router and turn off wifi I can see iOS's wifi daemon pull and scan local network device BSSID's right out of thin air in console while I have the iPhone locked. This data can be used for trying to find a preferred network and location information....
Speaking of location data, Apple not only uses BSSID via crowdsourcing to help determine locations but iOS also uses the network's RSSI as a way to determine movement. With a high enough resolution and monitored frequently enough (every 2 seconds as you can see in console) the change in signal strength from the router to the iPhone will indicate movement by the user as the signal strengthens and degrades. Again the iPhone is locked.
(isMoving, 1) = without turning on a single sensor iOS can determine I'm moving and act accordingly (wake up, background app refresh, apps that use geofence data, etc).
Back to the topic, the iPhone always has a very good assessment of local wifi devices and conditions on networks around it, regardless of whether you are in the settings wifi screen or if the device is locked in your pocket. The wifi chipset spends just as much time doing things when your not using the device than it does when you are...
If the iPhone isn't associated with a network it will actively probe networks fairly often (<1-5 minutes) by using a wifi standard protocol 'Probe Request Frame' (PRF) which is used by wifi clients connecting to Wifi host. But even if the iPhone IS associated with that network it will still actively probe networks depending on certain criteria. For example if the iPhone is asleep or the its RSSI to a wifi connections drops to ~-75dbm. This is to transition to a new data connection if the current one fails as seamlessly as possible, thus requiring knowledge of the network PRIOR to a disconnection. Apple vaguely mentions this in their security white paper...
Actively probing a network is easy for the network to see. Its also easy for anyone that is looking with the right software to see. Again, this is a sleeping iPhone actively scanning....
Apple prevents privacy concerns by randomizing your devices MAC address and the wifi frame used with the access point. So while its easy to see, its very very difficult to isolate and track. So its ends up being easy to see but hard to track in practice.
The iPhone can use passive scanning for wifi but its usually used when it needs to be, like with certain bands (unii2e) that are protected by 802.11h protocols and don't respond to Active probing. While a passive scanning will be more low key its a very slow, with a unii2e and some bad luck it might take 60-80 seconds just to start authorization for association meanwhile the iPhone can already be associated with a wifi network and in a power save mode (pretty much inactive but on the network).
Anyway, point is the iPhone and other smart phones are mobile devices and roam wifi networks constantly receiving data for various things like notifications and such. So they not only need to be able to detect and connect to a network, they need to do it power efficiently all while have a good assessment of other APs
on that same network or another local network (or cellular) so it can switch as seamlessly as possible, often maintain multiple connections at once.
