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Theoretical question --

Two Protec (or Protec 2) padlocks keyed alike. One lock is cut and stolen.

Does this make the second (non-stolen) lock vulnerable to someone making a key by analyzing the stolen lock?

I don't see why it should not be possible.

Yes, certainly possible.

Although having a locked padlock stolen by cutting it is not entirely preventable, some large institutions (hospitals, universities, etc) do take measures to prevent cylinders from leaving their control. For example, a university has an off-campus building no longer needed and will sell it. Before putting it on the market, the campus lock shop will strip all interior doors of their cylinders (they can leave the rest of the hardware on if they so desire) and all exterior doors will get replacement cylinders (usually aftermarket SC4 or Y2) for temporary security when the building is sold. Then it is the responsibility of the new owner to decide what to do.

I have heard of a university campus (I don't remember where) that had all doors that are normally unlocked (such as rest rooms and dorm living rooms) keyed alike, off master. That way, because stealing cylinders on open doors is easy, if one were stolen it would not lead to making a master key.

Easy to decode, but harder to find a key blank with the correct profile and the machine to cut it.

If I can get a Protec lock of the same profile with keys, I would fill up the cuts where necessary with hard solder and file the cuts. Probably it would even work with some epoxy. If the right profile is not available maybe it is possible to make a skeleton profile from an available key.

If your insurance found this out in the UK they would fail your claim.
I always try my best to talk customers out of keying alike for this reason, loose a key and every lock has to be changed.
A key can easily be originated from your missing padlock.

It's also worth noting, that unless the remaining lock is a PL321, it can be rekeyed, which can save you quite a bit if you choose to replace it.