No.  The system will not POST without a working, recognized screen.  
I had purchased this product Dell vostro 15 3568 in 2017. Recently the screen has become faulty showing only half the portion. And to make it worse the laptop was used very badly  and the hinges have come out and cannot be fitted back. So I thought of using it as a Desk top using another monitor via HDMI cable. But if I remove the display cable and wireless cable the laptop does not boot fully and shuts down because it is not seeing the display hardware. Is there any way I can use the laptop with the screen display cable removed?
Vostro15 3568