Yes the B777 with Trent engines can start both together, and it is regularly done.
This engine starts quite fast, takes around 30 secs to idle, if the engine was cold.
If the engine is hot, the FADEC will not select fuel/ignition on until the EGT falls below 100degC.
Some engines have a dry cranking time built into the autostart. The V2500 has for one. They call this de-bow as it is meant to allow the shafts to straighten out before ign/fuel on.
Modern engines do start much faster than older engines. The surge margin is much greater which allows you to put more fuel in for quicker accelleration. Listen to an old RB211-22B start up. The accelleration is nearly zero. and the engine rumbles away for ages as it slowly accellerates.
I like watching the CF6-80E on the A330. With a good tailwind, the fan is still rotating backwards at light up, which the GE
FADEC allows much earlier than RR