No, but if there is a red cross on white on a sign, it's good to know it's not just advertising from back before the region became a warzone.

How long before?

http://upload.wikimedia.org/wikipedia/commons/0/0d/Knights_T...

Both the cross of the Knights Templar, and the similar Maltese cross used by the Knights Hospitalier are quite distinct from the straight cross the Red Cross uses. I very much doubt anyone anywhere where variations like that are likely to be seen would confuse them.

And that makes it impossible for it to be protected as a trademark?

I didn't say that.