Is it possible for someone to discover the IP and/or MAC address of my mobile device, even if I do not attempt to connect to their network?
Yes, the MAC address can easily be discovered, but your device won't have an IP address unless it's connected to some network!
Let's assume that you are not connected to any network.
The attacker can discover your MAC address by sniffing on monitor mode, because your phone is probing for pre-associated networks, and the attacker can easily find the MAC address through that process.
And for the IP address, if the attaker is on the same Wi-Fi, then Yes, but if you're on a different network, I don't think he will be able to get much from that IP address.
When you use a mobile device to connect, especially in public areas, you have a more important thing to worry about: be careful to connect to an evil twin access point (called also: rogue access point or fake access point) where not only your IP/MAC address is seen but also your whole traffic.