Separate copper remover necessary for jacketed hollow points? (WWB 147gr JHP)

This may be a dumb question, but do Winchester white box JHP's deposit copper at all? Because I'm trying to decide if it's necessary to buy a separate copper remover solution on top of the regular powder fouling cleaners like Hoppe's 9? I'm going to be specifically using the WWB 147gr JHP's (USA9JHP2).

Indirectly, I'm basically asking if JHP's in general deposit copper to warrant a separate copper remover solution, if they deposit copper at all.

Here's a link to the product if you guys don't know what it is:

Winchester USA Centerfire Pistol Ammunition USA9JHP2 9 MM For Sale

It may leave some copper, but try cleaning lead from a barrel. Chrome lined barrels are a breeze to clean, standard barrels not too bad, all depending on how dirty the barrel is and how long the barrel has been dirty. Anyway, if Hoppes and a good copper brush or synthetic brush for a chrome lined barrel doesn't work I'd be surprised. To be more specific, copper bullets leave minuscule amounts of copper if at all, mostly what you'll be cleaning is powder residue, thus copper bullet residue is the easiest to clean in my opinion and I'd pass on any type of copper remover.