Yes, the frame works just fine without a Wi-Fi connection!
The Wi-Fi connection is only required to transfer new photos as well as to update the software. Apart from that, everything works the same whether the frame is online or offline.
We get a lot of positive feedback from users who set up a frame at their home, load it with photos and then gift it to someone without a Wi-Fi connection. Then, whenever they visit the household without the Wi-Fi, they can connect the frame to a smartphone hotspot and simply transfer photos while the frame has an internet connection.
A Short Tip
The frame may display af notification in the upper-left corner of the display to let you know that it has no Wi-Fi connection. To get rid of the notification, simply tap the x, or disable Network connection notifications in the settings.