I have observed that some songs containing ghost notes have 2 such notes together, each note played on a different string. Let’s say, for instance, that two consecutive ghost 16th notes are shown, one on the “E” string and the next on the “G” string. How critical is it that those notes are played as written instead of just playing both notes on the same string? Would the “thud” sound really be that different?

The only difference I could see would be the harmonic value, although if your tone isn't blaring then it wouldn't matter all that much.