alosaurus,
In the simplest terms WGS84 is a grid system used by GPS based on the position of true north in 1984. Your GPS position is with reference to this grid.
Now imagine taking your chart and drawing the lat and long lines a little offset to the north and west. Your gps tells you you are N10W10. on your chart using the original grid there is a navaid at this position but because the GPS grid and the charts grid are not the same when you tune the navaid you find it is displace from your position by the difference between the two grids.
Any navaid based procedure will have you at the appropriate position because it's based on the grid used to define the navaids position and your position is referenced to the navaid.
If you try and use an RNAV system that is using GPS as it's position solution on a procedure based on a different grid and ground based navaids, you may well find yourself offset from where you should be. And this may put you somewhere unsafe.
Some aircrafts AFMs specify that GPS position updating is prohibited in areas which are not WGS84.
So you shouldn't fly a radio based procedure using only GPS based RNAV without using the navaid raw data to confirm your position unless (as is the case in many places) the local regulations allow.