Suppression for the common citizen isn't about stealth like in the movies, it is about protecting your hearing. Guns are LOUD. Much louder than you expect.
Will deffos put you on a list but yes, absolutely. I wish the tax stamps weren't so high because morons who knew nothing about firearms were trying to score "I'm doing something" points.
Ask any service member who's probably still fighting with the VA because their hearing loss and tinnitus at age 38 is deemed "Not service related."
That being said, these electronic earmuffs people are mentioning are the bee's knees, so you could invest in a couple pairs of those and a poopton of batteries for the same cost as a suppressor, and still have enough left over for other important things, like a first aid kit.