Chosen Solution
Will computer work with no battery installed when plugged into wall?
Sorta! Can your old mustang drive with only two cylinders working in the engine? Sorta! On a flat road at a slow jerky speed! Now will it go up a small incline or hill? Nope! Your system is in the same plight! Running on the limits of the MagSafe’s power output which if you are running something which pulls more power than it can offer lights out! You also risk corruptions to your drive! Its even possible to damage your system in this state! So if you are trying to diagnose if the system is working (not running anything other than the OS) then it can be useful diagnostic to help isolate what the problem is. Beyond that you are playing Russian roulette! So the bottom line - Don’t!
It should work - albeit with several handicaps. I know someone who spent a while using his MBP on a charger without the battery. The computer’s performance will decrease by quite a lot, and as the answer above states you risk corrupting something. Especially if all you have is a 45W charger.
