I'm sat at my desk at home now with my work laptop on my desk, my personal desktop next to me powered off with the keyboard and mouse tucked away, the laptop is plugged into my personal monitor so I can have two screens.
Even if I was allowed to I wouldnt want to use my personal desktop, I've gone to the extreme of keeping them both separate and spent a fair bit of money on cabling, cable tidies Monitor riser etc just to be able to have them both share the relatively small desk. Reason being is what Haggisman said, the amount of work related apps that I'll need to install and configure to connect it would take forever just to get it all configured "Dont mix work and play" applies