Yes, pops/ticks from the vinyl/stylus pickup is a different issue than residual noise floor from your active components, and ground hums. Indeed - cartridge quality (especially stylus profile), condition and grade of vinyl, phono stage, and overall vinyl/stylus hygiene quality will determine how annoying or innocuous these noises are. As Terry mentioned, Ralph of atmosphere has long posted some very interesting information on the subject of phono stages, and how some designs can greatly exacerbate the pops/ticks issue (I believe he mentions overload capability and recovery - i.e. you're not hearing the actual aberration on the vinyl so much as the amplifier's poor handling and recovery from it).
Speakers themselves should not directly affect the perception of pops/ticks, unless they have an emphasis in the frequency ranges of these unwanted noises - those may not be the best choice for a vinyl system..
I started out with a Benz Glider and the pops/ticks were there, but did not significantly detract from my enjoyment of vinyl. Then I got a Ortofon Kontrapunkt "c" (Fritz Gyger 80 stylus), and wow! The noise floor dropped, along with pops & ticks. Another year later, and I hear my first Koetsu - it was a revelation how quiet this cartridge was, not to mention the rest of the sound quality. I still run Koetsu as my favored cartridges, but I’ve also been particularly impressed by the top Shelters’ (Accord and Harmony) exceptionally low noise. And I use a Clearaudio Double Matrix Sonic pro for cleaning vinyl, and a Magic Eraser for the stylus. A good vinyl record is as close to a living performance as I care to imagine.