Assuming you mean Level Shift and not the Incarnate Shift, since the Incarnate shift only applies in the Incarnate trials, where the enemies are always above your level, no, it doesn't affect rewards.
From the wiki page:
"While this is equivalent to Combat Level 51 for the purposes of combat, all other aspects of the game that depend on character level are still calculated for level 50. This includes rewards (a level 50 (+1) character fighting level 51 enemies will receive the same Inf as a level 50 character fighting level 51 enemies) and any Sidekicking (a character Sidekicked to a level 50 (+1) character will be Combat Level 49)."
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Does this effect rewards at all? Will a blue con while being 51 give the same rewards as if I was 50? Does it effect shard drops or anything which require an even level mob?