I did the experiment, and the answer is yes, it can be done! It ain't really pretty, but you didn't ask for pretty! ;)))
I happened to use material from thin surgical type gloves (non-latex but stretchy):
You'll need some kind of tube (I used the body of a low D penny whistle, sans the usual whistle head --- just a tube with six finger holes in it), gloves or other suitable material, scissors and elastic bands.
Cut two strips from the glove and lay them over the business end of the whistle body. Secure the elastic bands to hold the membranes in place.
Experiment shows that the membranes will not work if they are placed side by side like vocal cords. Here you can see what vibrating vocal cords look like. Space between these elastic membranes won't make a sound, however.
I found that overlapping the two membranes slightly gives a nice wounded duck sound. Almost musical in nature! Slightly overblowing gives a crude goose call sound. Blowing very hard makes the instrument really bark.
The holes in the whistle allowed for perhaps two or three good notes, and a whole lot more crappy notes.
This basic technique also works on brass instruments. Interesting sounds all around, but probably not stable enough or easily enough controlled to be of much musical use. Perhaps...
You'll have to do your own experimenting and hear what possibilities present themselves!
Stretch squares of rubber over different lengths of mailing tubes. You can tap the membranes like a tubulum, or you can blow on and across the membranes. This gives a slightly windy, rushing tone. Giving a good strong puff of air creates a slightly percussive attack. Different volume tubes yield different pitches.
A third possibility:
Using a single piece of vibrating diaphragm, make a diaphone! I'd hazard the guess this could be made into a useable instrument. And this example actually sounds pretty good!