Yup. Nails are soft, screws are hard, and those bits (and the Erwin ones, as long as you buy the correct ones)) are defo rated to go through nails; I have these and they plough through nails with relative ease.
Screws is a very different thing as there’s nothing other than diamond that eats those.
The Starret bits do go through, but after a few holes / screws you’ll defo see the teeth beginning to fail. I treat these as a consumable and just but multiples of the go-to sizes and bin when they start to struggle.
Same with flat wood bits, just buy cheap ones off amazon, boxes of multiples of 12/16/20/25/28/32mm and treat as disposable.
If the know there’s a screw, try to remove it, if you’ve gone through nails, whack a screw in after to reinforce what you’ve removed.
Another joyous day of house-bashing.
These are the best ones imo, if you’ve a whole house to 1st fix for plumbing and electrics. LINK