A P/A, workload permitting would be in order or at least call the CA1 to put him/her in the picture. Sometimes though the ATC workload can increase significantly for PNF as he is following A/G instructions to rejoin the existing (full) pattern, especially LHR. The PNF/PF will have their hands full reconfiguring the aircraft so a P/A could/may slip down the order of priorities.
The passengers would notice the G/A since flaps/gear etc would have trundled out, various power changes, then smooth on the approach followed by an abrupt power/pitch change to follow the missed approach procedure. Generally you aim to maintain your intermediate approach speed in the climb so massive power changes aren't required, no swooping up or stuck in the back of your seat rides. Climb away at 1500 fpm, accelerating according to flap retraction speeds and then leveling off at the missed approach height, following ATC or as the charts prescribe.
Fuel figures for the B767 for the go-around, circuit and subsequent landing is only around 1.5t, larger aircraft will require larger power gradients and therefore larger fuel consumptions.