I have wondered this for years. Could an aircraft successfully take off with the flaps fully extended to the landing position? To make this more concrete, let's say a B773-ER at ATL runway 8R.
Given the right weather, and takeoff weight, yes it could leave the ground. Will it be able to attain the regulatory climb gradient? Probably not. Will it be safe in case an engine fails? Most definitely not.
Landing flaps add lots of drag. That's why they are retracted during an aborted landing for example.
On takeoff, too much flaps means you can stop easier if an engine fails. But it also means you need longer distance to accelerate if the decision is to continue. That means the go-speed will be slower than the stop-speed. See: How is minimum runway length related to V1?
There can't be two decision speeds. Limiting the flight to the slower go-speed will significantly limit how much fuel/payload the plane can carry. And of course if an engine fails during the initial climb, the remaining engine won't be able to keep the plane climbing at a safe rate.
Manufacturers test the different configurations in all conditions, such as weight, runway length, winds, etc. After the data is collected, and with some interpolation, the takeoff and climb performance tables are produced and approved by the regulatory bodies. Any configuration used that is not approved would fail the regulatory and safety requirements, and put everyone in great risk.
The answer is yes it can, the B773ER regularly takes off at flap 20 setting and can performed a go-around at Flap 30 (although the procedure is to raise the flap to 20 immediately).
Taking of at Full Flap (Flap 30) is well within its capability, depending on how heavily it is loaded, how high the airfield is, how long the runway is, how hot the temperature is and how steep the required climb gradient is given the surrounding terrain.
There would be a warning sounding in the flight deck during the takeoff, as this is not a normal takeoff configuration. When the aircraft accelerates above 180kts in the climb out the flaps would automatically retract a stage to protect themselves against the aerodynamic loads