Sure, but bonding one sheet to the next overlapping one might "foil"
your goal. Few of us with dominant Y genes realize that aluminum foil
is wax (an insulator) coated on one side.

I understand it's typically a very thin plastic or paper, to which the
aluminum is laminated

It is just plain aluminium, no wax, no paper, no plastic. Just think of the
results if you cooked something wrapped in a foil with a wax or plastic
coating!!! The matt finish on one side is just a result of the way that the
foil is rolled when being manufactured.

Jeff