On the 777s I fly, firewalling the thrust levers (or selecting TOGA once airborne) will result in max rated thrust - period.
As others have said, Vmcg/Vmca are based on the applicable thrust rating (ie TO, TO1 or TO2), so theoretically it should be safe to increase the thrust up to the fixed derate, but no further. That's ok when using TO with an assumed temp - pushing the thrust levers up will result in full TO thrust, but theoretically there shouldn't be any control issues as the applicable Vmcg/Vmca will be based on full TO thrust anyway.
The problem arises when using a derate (ie TO1 or TO2) with an assumed temp, in that the crew has no indication where the derate limit lies. Firewalling the thrust levers will result in full TO thrust and Vmcg/Vmca could theoretically be compromised. Hence Boeing's recommendation not to increase thrust when using a derate with an assumed temperature.
Having said all that, on the -200, -300 and -300ER, V2 is well above both Vmca and Vmcg even at low weights - don't know about the 200LR, which has the GE115 engines and the short fuselage. As Old Smokey said previously, it should therefore be safe to select full rated thrust once the aircraft is above V2. Nevertheless, terrain clearance SHOULD be achieved without increasing thrust.
Two ways of achieving the extra thrust if desired:
1. Once airborne and above V2, press the TOGA switches. That will result in TO thrust and the removal of any armed lateral or vertical modes (ie LNAV/VNAV). The FMA will then annunciate THR REF / TOGA / TOGA. Once above 400ft, rearm LNAV and VNAV. VNAV will then then take care of the acceleration.
2. Once airborne and above V2, push the thrust levers up manually, then press the TOGA switches before 400ft, resulting in THR REF / TOGA / TOGA. Above 400ft, rearm LNAV and VNAV as above.
Hope that's clear as mud!