YES
it is possible but it is very rare, the chance is 1/8192.Another reason it's possible, Uxie doesn't belong to the illegal Shiny Pokemon.
Unobtainable Shiny Pokémon
In most generations there are a few Pokémon that cannot be obtained Shiny without cheating or glitches, due to either being distribution-exclusive without an in-game location or, in Generation V, being programmed so that they cannot be Shiny in the wild.
Generation II
Mew
Unown forms other than I and V
Generation III
Celebi
Generation IV
Celebi
Spiky-eared Pichu
Generation V
Celebi
Victini
Reshiram
Zekrom
Keldeo
Meloetta
Genesect
