Yes... This is absolutely possible. I infact did this with two of my laptops that had hinges broken. Of course, I had to give up the in built wireless functionality, webcam and internal mic.
My first laptop was an MSI A6005. Removing the hinges was quite easy. Removed the LVDS cables, wifi card and antennae and webcam connector from the mobo. Screwed everything together and connected it to VGA and voila! I see the POST screen and windows booting on my external monitor.
The second and most recent one (last week) was an HP laptop. This was a tricky business. I've opened HP laptops in past and I'm not a huge fan of it. After removing the screen and screwing it back up, it did not start for sometimes. I re-opened it, checked the connections and tried to boot and I see lights come up and fan start up, and immediately stop. Lights still on and hard drive still spinning. I attach an external monitor and don't see anything either. I had to open it again and connect the display and power it on while open to see if it reports anything to the screen. Turns out, I need to press enter key during POST to get past a missing wireless card warning message. After that, it continues windows boot and once it boots windows correctly, it identifies a secondary monitor and sends signal to it. So after screwing it back together, I started it, pressed enter while it was connected to external monitor. It still refused to show anything until windows booted. This could be programmed in the HP firmware.
But in short, it is absolutely possible, but you may have different results depending on your laptop manufacturer. My MSI allows me to change BIOS and see POST messages on external monitor by default. HP on the other hand does not show anything on external monitor unless it boots into windows.