No note, and the same for Patti. However, as I recall from the summer of 2007 some who merely wrote Angie or just asked for a signed playbill (she threw one of those into my package, by the way, what a doll!) did get copies of the same note that went something like this:
Dear (insert name), Thank you for your lovely letter. Your encouragement has given me a renewed burst of energy to continue acting.
Love to you,
Angela Lansbury
So it really depends upon the performer.
I say, if you really want Carole to send you a signed headshot, ask her directly for one. Ask her also that if she doesn't have one to send you a signed playbill in its stead.
Just be sure to use tact and you're practically guaranteed to get one of those two.
2010
Feb. 28 - Looped, Feb. 28 - Next to Normal, March 4 - Hair, March 11 - A Little Night Music, March 24 - Time Stands Still, April 6 - La Cage Aux Folles, April 10 - Anyone Can Whistle (City Center), April 10 - Looped, May 9 - Enron, May 15 - A Little Night Music, May 15 - A Behanding In Spokane, May 30 - A Behanding In Spokane, May 30 - A Little Night Music, June 20 - A Little Night Music, June 23 - Red, June 23 - Sondheim on Sondheim, July 13 - A Little Night Music, July 18 - The Grand Manner (Lincoln Center)