Nope. Especially not the lower end HPs. They have gone back to their old ways of using non-standard power connectors so they aren't even upgradable or repairable.
HPs and others like them are cheap because of the tiny cheap case and discount on the OS that they get. You'll want a decent case and probably not 9 billion pounds of bloatware on it so starting with an HP at the core isn't great.
You can build a decent gaming rig pretty cheap, especially if you have some parts that can be carried over from an existing system like the monitor, mouse, and keyboard.