Answer: Probably not
A lot of people are concerned others will notice their cage when they start wearing it. You’ll be far more conscious of it than anyone in your vicinity. If someone did notice I’d be far more concerned about why they were looking at my crotch intently enough to notice a cage than the fact they’d seen it.
Do you regularly stare at peoples crotch trying to see if they’re wearing a cage? Maybe you do… who knows…
Unless you’re wearing a particularly bulky cage with a massive padlock hanging off it it should be practically invisible through your clothes. Cages are designed to be close fitting and discreet.
If you have an externally locking cage you may want to use plastic numbered locks to reduce sound of a metal padlock hitting the cage. However, many cages now have internal lock systems which remove the need for a padlock.
The only time the chastity cage might be seen is if you have skintight gym clothes on. I’d recommend removing the cage for intense exercise anyway so it shouldn’t be an issue for you.
With cages becoming more and more common it’s about being confident with your new accessory.
Please don’t recommend this cage. Your foreskin gets caught in it.