Can the Roku app connect without WiFi?

Yes.. exactly what the previous reply said, the official Roku app and all 3rd party apps require a wifi connection. 

Both the Roku and the App (your phone) need to be on the same wifi network ( eg.. DORM 2)..

There is one thing that I just thought of.. 

Check with the person who has access to the router itself / configuration / Dorm supervisor... see if they can add both your Roku and phones MAC Address (to the same wifi band/ SSID  / streaming network. Create a whitelist rule  in the advanced connection section that will always allow both to connect to that particular channel.

If so.. connect both devices to that network, then make sure your phone is set to default to that network (this is so it will save the connection info) ...

oh and just thinking about it right now.. since you are going to be listening through the remote, put the remotes Mac Address on the same network.. you can get the Mac from the Settings > Remotes & Devices > Remotes >select the remote then go to About.. and the Mac Address is listed

I say to add the remote to the router network just to cover all your bases since there are several networks

This should work.. if not.. then they probably have some strange configuration..or they have several configurations for all the different types of devices .

I've done this not only in the same environment but also at hotels (Vegas) and even at home and it has always worked. 

I hope this helps and works for you and Happy Streaming!