Reference "The Litton Pilot's Guide TP92-0413G, Rev 10"
"When the FLUSH mode is selected, all position updates (GPS, RNAV, TMIX, MANUAL) will be zeroed and all three automatic updates will be disabled. The system will use inertial position for horizontal guidance." see page 6-26
"Disabling TMIX assumes a problem with the triple mix solution and will flush the TMIX corrections from that INU (this has no affect on other INUs and does not flush previous GPS or RNAV corrections)." page 6-18
So, the answer updates are not flushed unless the operator commands it throught he FLUSH MODE.
As far as the snaking goes when coasting in and getting a RNAV (DME update), there is an "EASY ON/OFF STEERING" mode:
"To enable a smooth and easy trasition, the HSI/Autopilot steering to recapture desired Track is limited ot a maximum rate of 1.9 nm/min. This "Easy On/Off Steering" causes shallower slower maneuvering during track recapture." page 6-1