IIRC you can use wifi to download map app and maps but without the help of the phone towers the GPS can be a bit slow and not so sensitive
The phone still connects to the transmitters, even without a SIM - you can also still use the phone for emergency calls.
In any case, the phone's built in GPS is always the most accurate system, they use the same chipsets as stand alone sat navs If you are using the phone as a satnav, the app will turn on the internal GPS. The system using the phone towers is used as an alternative to save battery power, but is low accuracy and not suitable for navigation.
In my experience, a phone works every bit as well. OH uses TomTom on the phone, and once running, it's just like a dedicated satnav. I keep it on my phone just as a backup, as I have one built into the car.
Also, if you want the addition of live traffic data for these apps, you can still pick up pay-as-you-go data sims for three network which give you 200MB of data every month free, without any top up - 200MB a month is plenty for traffic data.
Sygic GPS is a popular free app for android.