I just tried this and it says 'Accessory not supported' on the iPhone 15 Pro Max with iOS 17.0.3.
All official Apple accessories. I have a lightening cabled SD card reader that I've used with my past several phones. I have the lightning to USB-C adapter that I bought for other purposes with the iPhone 15 which do work.
I was also hoping this worked because it would have saved me having to buy yet another adapter.
I also tried this on my Windows PC and it says the USB device is unrecognized although it does show up in device manage as a 'billboard device'. It is unable to find better drivers for it and I don't care to dig around for any. Just mentioning it doesn't work on a PC either.