I've user tested a captcha precisely one time, but I'd argue that yes, it does make sense. Many, many people still don't know that bots are capable of submitting data via forms. Therefore, they are also unfamiliar with the concept that bots submitting forms is undesirable. And they are thirdly unfamiliar that tests for sentience exist and are necessary.
Because of all that, you need an instruction with a captcha.
Many first-time web users are 60+, and I've seen them struggle with understanding the difference between AOL, the internet, and their email addresses.
Show my elderly father a captcha, for example, and he knows he has to do it but he doesn't know why. He's not new to the web. He knows just enough to trade stocks, to email people, and to read Fox News. He usues captcha but doesn't know why it's there; he certainly doesn't experience a sense of security when he sees it. He experiences annoyance. We've talked about captchas before; he knows he has to prove he's a human, and therefore that bots are capable of filling out forms, but he doesn't know what can result from that or why it's undesirable.
TL;DR: Not every user is a 20-something who grew up looking at captchas.