No... As a reader of the comics and owner of the game i can definitively say that the game comes after year 5 of the comic series. It's even in the description of year 5's comic

No hardcover omnibi that I'm aware of but there are regular hardcover volumes.

Injustice: Year One

Injustice: Year One, Vol. 1

Injustice: Year One, Vol. 2

Injustice: Year Two

Injustice: Year Two, Vol. 1

Injustice: Year Two, Vol. 2

Injustice: Year Three

Injustice: Year Three, Vol. 1

Injustice: Year Three, Vol. 2

Injustice: Year Four

Injustice: Year Four, Vol. 1

Injustice: Year Four, Vol. 2

Injustice: Year Five

Injustice: Year Five, Vol. 1

Injustice: Year Five, Vol. 2

Injustice: Year Five, Vol. 3

Injustice: Ground Zero

Injustice: Ground, Vol. 1

Injustice: Ground, Vol. 2

Injustice 2

Injustice 2, Vol. 1

Injustice 2, Vol. 2 (out May 1, 2018)