I do not think they have the ability to find\track you.
The first thing they ask for is a contact number to call you back on in case the call drops and then they ask your location (Address).
I called them a few weeks ago regarding my son and they asked me the above details.
IIRC the reason they ask for the number is specifically for the call back so if it drops they guarantee a way to contact you again as in some situations you may not be calling from a phone you have normal access to or because if you call with a sim they can't call back, the call number or other ID is always logged by default. Basically it's confirmation of the number you want them to use to contact you if needed most of the time, but in the event of you calling from a device without an active sim it becomes the only number they have to contact you again. It's a belt and braces approach that allows for the edge cases.
Any mobile phone is in theory able to contact the local emergency services with or without an active sim or subscription, from memory that has been baked into the specifications since the very very early models (possibly the start of the digital mobiles), and is part of the reason you may not be able to make a normal call because your provider doesn't do service where you are (or are out of credit), but it will use any available operator and their systems have to accept (IIRC at a high/very high priority) any attempt by any mobile to call any of the emergency numbers*, as the call is then made using the IMIE of the device.
The emergency services can track a mobile by the IMEI but it's harder/more time consuming than if it's got an active sim** , what they can't do is call back on it as the active sim is what gives the mobile network the ability to actively route billable events etc.
In short.
Mobiles don't need to have a working number/sim to call for help or be tracked. They cannot however be called back if they don't have a working sim and the emergency services ability to do things like find the location of your call is impeded but not stopped (they fall back to older tools).
*IIRC 999, 911 etc are all registered and usable these days regardless of where you are because it was recognised that people with mobiles are likely to take them abroad where the emergency number may be different.
**IIRC if it's got an active sim they can potentially get the phone to report it's GPS, if they're working with IMEI they may be reliant on what the mobile phone towers say which is basically "the phone is in this area general area" as opposed to "the phone is within few meter of this specific location".