I’m learning a new piece of music that has a couple of Grace notes in it which has led me to wonder if it had a unique use or were there other ways of writing the piece using, for example, a one hundred and twenty eighth note to achieve a similar effect.
There is an element of uniqueness to a grace note, yes. When they where originally used in music, prior to the ability to record music, the length of a grace note was heavily dependant on a given conductor's interpretation of the piece, with the real truth sitting with the original composer. Grace notes are an example of Ornamental Notation and as a result, many modern composers choose to convert them to Literal Notation to prevent ambiguity.
As an aside, an interesting use of Grace Notes that could give some insight into their length is on instruments such as the Bagpipes where the chanter (the pipe part with holes to cover with your fingers), is continuously supplied with air from the Bag. This means differentiating between notes at the same pitch can be difficult or even impossible without something to break them up in between. Grace notes are often used here, and are supposed to be kept as short as possible.