You mean, a laptop that can use a remote-desktop app? Yeah, sure, pretty-much any of them can. Note that you might have some minor issues, if the screen resolutions of the two PCs don't match up.
You need a version of an OS that supports Remote Desktop Server on the PC you are attempting to control, or you need to install something like the TeamViewer Service.
I tried using teamviewer to control my desktop with my phone, but it kept asking me for a password each time. Any way to make it sync with the controller laptop I might get?
Do they sell super cheap laptops with a decent screen and keyboard for this purpose? A controller laptop