Let try to clear a little bit here ... read carefully and do not interpret ... Boeing folks are lawyers but not stupid
- With speed less than 50 KIAS, pushing a TO/GA switch activates the autothrottle in the thrust reference (THR REF) mode. The thrust levers advance to the selected thrust limit. If the autothrottle is not active by 50 knots, it cannot be activated until above 400 feet.
- At 80 knots, the autothrottle mode annunciation changes to HOLD (and will stay in HOLD until 400 ft AGL when it'll change to THR REF).
- With speed greater than 80 knots, pushing a TO/GA switch disarms LNAV and VNAV.
After lift-off
- if a TO/GA switch is puched:
- removes takeoff and climb derates and assumed temperature thrust reduction
- A/T in HOLD, the A/T activates in THR REF.
Now ...
The autothrottle is in HOLD between 80 knots and 400 feet AGL. Take-off thrust (THR REF) must be reached before 80 knots and ...
.. in a normal take-off after takeoff thrust has been set, you shouldn't touch the thrust levers until or as early as 400 ft AGL (minimum altitude at which by regulation you are allowed to apply the first thrust reduction).
Engine Failure during an ATM, if more thrust is needed, thrust on the operating engine may be increased to full thrust by manually advancing the thrust levers while still on the runway, or by
pushing the TO/GA switch when airborne. This is because the takeoff speeds consider VMCG and VMCA at the full rated takeoff thrust.
Engine Failure during a Fixed Derate, increase beyond the fixed derate limit could result in loss of directional control and should NOT be accomplished unless, in the option of the captain, terrain contact is imminent.
Engine Failure during a Combined, behave like a Fixed Derate.
And for the records , 400 ft AGL is also the minimum altitude at which you are allowed to iniziate a turn in case of a partial loss of thrust (for obstacle clearance) (so called Special EO SIDs). Airbus or Boeing ... you will not be able to obtain you minimum certified obstacle separation in the first and second segment climb if a turn is initiated before 400 ft AGL.
Now am I correct in that by NOT selecting TOGA the HDG select and TRK select are not available until 400ft? This making an emergency turn below 400ft difficult since the flight directors will still command the LNAV profile after 50ft which could be at odds with an emergency turn?
Autothrottle system is different from AFDS and yes you cannot select any roll mode (including HDG/TRK) as low as 400ft AGL, but you shouldn't because you loose lift in a turn. In the Takeoff Logic the airplane will maintain rwy heading or extended rwy track if the two defers of more than 0.7 deg.
You shouldn't perform any emergency turn below 400 ft AGL unless you are following VFR which you and you only are responsible for your obstacle separation.