Arguably, the pedal would be applied after the grace note when notated like that. However, musically it makes more sense that this grace note is more of a "fingering" instruction, with the desired effect being what you spelled out in your second diagram, an on-time three-octave E though with a slight glissando and held via pedal.
However, if you try this exactly timed as written but without the final two notes, you'll find out that pedalling right after a short low note will have an interesting echo effect. Striking the final notes will mostly mask this, however. Playing around with such sound effects should really be done on an acoustic piano since it's anybody's guess just how much of those side effects a digital piano may or may not model.
Now for figuring out the indended effect, it might also be interesting to see what happens in the right hand at that time. If it is basically silent, the likelihood that the left hand is supposed to do some acoustic trickery is higher.