So if an autopilot flight plan intends for a plane to be at a certain location vertically and laterally at a given moment during enroute flight somewhere within WAAS coverage, one can expect that their aircraft will acheive this placement within the stated WAAS accuracy?
No, that's not a reasonable expectation. The WAAS accuracy relates only to the accuracy of the position solution out of the WAAS box, known as Navigation System Error (NSE). You then have to add the Flight Technical Errors (FTE) which relate to the ability of the aircraft to follow the WAAS guidance. Generally for WAAS, FTE dominates NSE.