Last tested: May 7, 2021
Not natively. If you allowlist specific IPs in Looker, then the IPs of mobile phones won't be able to reach Looker. Mobile IPs are temporary (change every few days) so allowlisting the phone IPs isn't a sustainable workaround.
Workaround: Use a VPN on their phone to connect to a static IP that can be allowlisted.
Feature Request to comment on: https://portal.feedback.us.pendo.io/app/#/case/60895