There is nothing in the rules to explicitly legislate against submitting a score from each 9 separately (and EG's system doesn't prevent it), but it could easily (and possibly rightly) be seen as an attempt to manipulate one's handicap record, especially when the intent is clear to submit scores for all 18 holes. As such, I would strongly advise against the practice, and suggest the handicap committee should possibly re-enter such scores as a single 18 hole score.
And a few points of note from others comments...
Both 9 and 18 hole scores have exactly the same influence on the handicap calculation, but two 9 hole scores will have more effect than one 18 hole score.
Due to the "net par +1" scaling, it is potentially easier to maintain a lower handicap with 9-hole rounds because bad scores will never be as bad as 18 hole rounds can be.
Handicaps are calculated with respect to the number strokes taken, and the Course and Slope Ratings of the course played. Strokes received have no bearing on this.
WHS handicaps reflect "average best", rather than just "average", scoring.
