Hm, that would be a cleric spell rather than a mage one. Anyway, I believe the answer to your question is yes, as find traps is supposed to emulate the thief trap finding skill, and as such should give almost guaranteed sceret door detection as well. I didn't test this myself though, so it's possible there's a discrepancy.
You can find secret doors without any spell or ability... just takes a while longer for your character to see it, and usually have to know where they are and stand next to them.
You have a 5% chance per round of finding a secret door, unless you're a dwarf or elf, in which case they get a 20% per round. Thieves using find trap, use their find trap score instead.
No idea if the spell Find Traps would do it, since it's a largely useless spell and I never use it.
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No idea if the spell Find Traps would do it, since it's a largely useless spell and I never use it.