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Per the Blood Angels Codex:
Shackle Soul
The Librarian reaches into the foe's mind, trammelling his
soul and crushing his will to fight.
This power is a psychic shooting attack that hits
automatically an enemy unit within 12". Until the end of
its next turn, the target unit must pass a Leadership test
each time it wishes to move, run, shoot or assault - if the
test is failed, the action cannot be performed. A unit that
fails a test to run cannot instead choose to shoot, and
vice versa.

Does Shackle Soul work vs. Overwatch Shooting?

Yes. Overwatch is a type of shooting.

I think a better way to phrase the OP's question is, "Must a unit that is Shackled pass a Ld test to fire overwatch?" Because otherwise it sounded like, "Can I use Soul Shackle when I fire Overwatch?"

 Elric Greywolf wrote:
I think a better way to phrase the OP's question is, "Must a unit that is Shackled pass a Ld test to fire overwatch?" Because otherwise it sounded like, "Can I use Soul Shackle when I fire Overwatch?"

The OP wrote "vs overwatch" which would mean "against" overwatch, not "while using" overwatch. Pretty clear

 Elric Greywolf wrote:
I think a better way to phrase the OP's question is, "Must a unit that is Shackled pass a Ld test to fire overwatch?" Because otherwise it sounded like, "Can I use Soul Shackle when I fire Overwatch?"

You cannot use psychic powers during overwatch.

Fragile wrote:

 Elric Greywolf wrote:
I think a better way to phrase the OP's question is, "Must a unit that is Shackled pass a Ld test to fire overwatch?" Because otherwise it sounded like, "Can I use Soul Shackle when I fire Overwatch?"

You cannot use psychic powers during overwatch.

No one said you could, and it is also quite clearly stated in the BRB that you may not.