Yes, you can log into your Togo RV account on multiple devices.
Your profile information and checklists will automatically sync between any devices you're logged into. Just make sure that you're logged into the same account in both places.
If you are not automatically seeing checklists or RV details synced when in the Home section of the mobile app, try pulling down on the page to refresh it. If refreshing doesn't help, please log out and back in and check again.