Note: I also used my aussie uber account (with no details changed) from a device (not my phone) with a UK sim in it in Croatia and Portugal last year, again no problems.
Uber only needs your mobile to validate the app the first time you use it, like i said unless the driver cant find you they don't call the number in the phone (and most use the in-app messaging first which only requires data).
Even at home, if my mobile is going flat I will will use my tablet to book an uber (completely different sim) with no issues.
Uber just needs internet connection and an account which has previously been validated.
What can cause issues overseas is your payment method. In aus i pay for all my Ubers using paypal. Paypal is not allowed for uber payments in croatia, so I had to use a debit/credit card (or weirdly cash is an option for uber in croatia).
I always roam with my aussie sim in my mobile (but with data turned off) and make no calls, so I can receive sms from bank if necessary (costs nothing to receive sms over seas) - so zero extra cost. But i always put a local (or UK with free data roaming) sim in my 4G tablet for data to use with apps while Im away.