Not always. It's up to their installer. And the installer doesn't have to ask (it can just do it).

The situation is better these days, with windows store apps. Still, I developed the habit of just never using the desktop in the XP days when things were really bad.

There was a war over your eyeballs, which had shady software vendors warring over desktop space, start menu space, taskbar space, even fucking file associations. I recall for a little RealPlayer and Windows Media Player used to yank back and forth file associations each time they ran, even if you tried to make them stop.

No one of my biggest complaints about windows is the sheer number of apps that add an icon without asking. Sometimes it's even worse than an app, and Nvidia or AMD will add one in a driver update. Drives me nuts.