I don't think so, Eric; to wit:

piece [n]
14 g. A passage for recitation; a short speech. Now chiefly U.S. and Eng. regional exc. in to say (also speak) one's piece : to have one's say, to express one's opinion on a subject or question; to make a statement.

1822 C. M. Sedgwick New-Eng. Tale vi. 85 The young woman was to speak a piece of her own framing.
1865 C. F. Browne A. Ward: his Trav. ii. i. 128, I have spoken my piece about the Ariel.
1895 ‘Rosemary’ Under Chilterns 83 All the ‘pieces’ that the children learnt to repeat at school they taught to her.
1941 U. Orange Tom Tiddler's Ground vi. 117 Lady Cameron was simply furious with me after that concert-party episode, when I just flatly refused to say my piece.
1973 J. Porter It's Murder with Dover xi. 115 ‘You didn't speak to Marsh again?’ ‘No. I'd said my piece.’
2003 Washington Times 9 Apr. c09 He..gives each caller a chance to say his piece before moving on.
[OED]