Yes, as long as the foil had a continuous electrical connection all around outside the box, and the inside of the box was completely electrically insulated from the outer foil shield, it would be a Faraday cage.

Depending on the strength of the external signal(s) you are attempting to keep out, a thicker outer shield and even grounding may be required.

Thank you for your post. Would the cardboard box the device came in be an acceptable insulator?

You have me real curious as to what you are doing with this
project.
Dry cardboard is an insulator but for how many amps I wouldn't
know. How many amps will be carried by this apparatus.

Pooh Bear

The insulation, as well as the shielding, really depends on the type of EMI you are trying to dissipate.

Are you trying to simply block nearby radio interference or attempting to block an EMP from a high altitude nuclear detonation, coronal mass ejection, or E-bomb?

Or, on the other hand, are you attempting to block external electronic eavesdropping of your own electronic devices?

I bought a wind up radio, that I am trying to protect from the possibility of a coronal mass ejection CME.

"Would the cardboard box the device came in be an acceptable insulator?"

Yes, unless you're way up north, normal/above normal CME activity is usually relatively weak once it gets down to non-connected electronic devices in the home.

You could either build a Faraday cage box to keep other devices in as well or just tightly wrap the radio box up in foil.