Will a car even run after you remove the battery while it's runing? I'd love to see a car run with no o2 or maf sensor. Id say it's sarcasm
Yes it will run as long as the alternator is working. I've changed batteries in Hondas occasionally with the engine still running so that I don't have to call the Honda dealer to get a 5 digit radio code. I don't make a habit of it, but nothing bad has ever happened. Long term it will put a huge strain on the alternator and you'll probably kill it. Taking 2 min to change a battery, not so much... just don't let the + lead touch a ground.
To the OP... The main reason the car is so much quicker when you are in open loop is that it is running off of pre-set maps in the ECM... when it switches over to closed loop you are now basing all the readings off of all the sensors, IAT, ECT, and O2 sensors included.
Did you know that when you have your throttle at 100%, it switches over to open loop regardless of temperature? Damn near every car does this. Also most cars will disable the A/C compressor when the throttle is at 100% as well just so you know.
To f1yen: when you did you 3rd gear accelleration test.... were you completely flooring it 100%? If not, that might have something to do with it as in open loop it is attempting to control emissions. In my experience/opinion it seems that cars in closed loop will be a bit "slower" to respond to throttle input changes... and my guess as to why this is(or seems to be to me) is because it's running off of a pre-determined map with all known values.... it doesn't have to compute the outputs of the O2 sensors to figure out how much fuel to dump.
Pretty much everything that
Mustard97 said is right on. Screwing with the ECT will make it run like crap unless it's reading the actual coolant temp(like installing a lower temp thermostat... which is also ******* stupid).
Why don't you watch your IAT #s from a cold start. You might find that the actual air intake temps has a lot to do with why it is a bit faster when cold... especially because it is a turbo car and after the intercooler gets heatsoaked, it won't be as much of a help. It's not uncommon for me to see 100-110 degree IATs on cars in the shop I work in after driving them on the road and bring them into the shop(which is kept at about 70-72 degrees). They will occasionally get down to 90-95 degrees if it is idling in my bay for a while. While moving down the road, they will generally be about 20ish degrees above ambient except for some cars that have very direct air intakes... such as Infiniti G35s.