Does Evensies work without a connection?

Yes, for most things. Your groups are kept on your phone, so adding, editing, deleting and restoring expenses and payments, commenting, archiving and adding names all work with no connection. Each change is saved at once and sent when you are back online, and Groups says how many are waiting.

Creating a group works offline too, once your purchase has been confirmed on this phone. So does saving an expense with a receipt: the receipt is attached once you are back online.

These need a connection: signing in, joining a group, making or stopping invite links, starting expenses with a friend outside any group the first time, deleting a group or bringing one back, choosing a cover photo, saving How you get paid, opening a receipt already on our server, an expense's History, the first exchange rate for a currency on a given day, buying or restoring the purchase, reminders, notification settings and deleting your account.

Don't sign out while changes are waiting: signing out removes them from your phone before they are sent, receipts waiting to be attached included.