Yes my cat can climb step ladders...even when they are folded up for storage.
She learned this trick in response to my husband's singing. It seems when he sings he hits the resonance for her skull or something because it just doesn't sit well with her. First she meows complaints and cease and desist requests with each request increasing in intensity. If he ignores that, then she attacks.
When we bought the house there were no stairs to the unfinished second floor. He was up there looking down the ladder at her. I suggested he sing to see her response. He busted into a rendition of "The Lion Sleeps Tonight" and once he hit that high note she had had enough.She approached said ladder and started climbing quite determined that the singing would stop when she reached the top. (That's my little evil genius.) After the wall thwacking incident we decided it was best if the ladder lived in the garage while not in use.