Once you've requested the trip you don't need WiFi any longer. During the request you specify the pickup location and the driver sees only that, not your actual real time GPS location, so whether you're still connected after the driver has accepted is not relevant.
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It matters for a few other things, which are minor: if the driver cancels you won't get that notification if you've already disconnected (so just stay connected until he's there or almost there, you can track him approaching your location while you're connected), also in some markets Uber has introduced in-app chat instead of calling, and if the driver is unsure of your location he might try contact you (in some cities, in developing nations especially in my experience, drivers don't come to the pickup location until you contact them to confirm where it is. Either distrust of GPS location that you entered or some other cultural issue, also at airports due to time restrictions on parking, useful to be able to call in such cases but I've often made do without).

I've used Uber in probably close to a dozen countries, often with just hotel or public WiFi as you describe. Not as ideal as having a SIM with data but it's very doable.