Not only can you access you Alexa app from both home network or any other wi-fi network, you can ajso access it from your cell data plan. We do this frequently.
Here is how to "simulate" testing access to Alexa from Timbuktu from the comfort of your living room.
First, turn OFF the wi-fi in your phone so your only access will be via your cell plan.
Turn on phone's Alexa app.
Now, send Alexa through her tricks to confirm what works. Also try other smart home apps (e.g. Kasa for smart plugs) to check that they work, too.
When you are finished, remember to turn phone wi-fi back on.