This is possible but the question is whether or not you want to trust it. Several issues:
1. If the PC doesn't start, you car doesn't start. This WILL happen to you.
2. Unless the PC is on standby, startup times are around a minute. You can probably get that down to perhaps 20 seconds, maybe a little less. Do you want to wait that long?
3. In a low battery situation, your PC will suck a lot of juice that could be used for starting. This could easily happen in the winter if your battery is older.
4. Your PC will need to survive crank every time to make sure the car doesn't shut off when starting.
These are not insurmountable problems but I'd bet money there will be times when your car will strand you somewhere. Most likely on an important work day when you have a presentation to the higher ups.