I am installing a remote car starter in my 300E and was wondering if the factory alarm will go off when the car is started with the doors shut and locked?

Since the ignition will have to be powered up to crank the engine, you will have some alarm interference. I would suggest just using the remote to lock the doors only without setting the alarm.

300e remote starter
 

I bought the remote starter for mine when I bought the remote keyless entry (see my thread...). After researching and then installing the remote entry, I decided that there was no way I was going to go thru the pain of the remote starter...