I doubt it. "I'll be damned," is more generic, and expresses surprise, while "damn your eyes" is directed at someone else and denotes anger, impatience, and extreme disapproval.

In the Hornblower books characters frequently shorten the phrase "I'll be damned" to just "Damme!" (Damn me!)... again, indicating surprise, shock, gobsmacked astonishment, and the like.

- LH