Not automatically, but you can do this with a script before you open the window:
-- Resizes this scrolling window to fit just inside
-- of the monitor, inset the customary 3-pixels.
-- For clarity, this handler performs no error-checking.
on OpenWithAutoResize aWindowName
put the screenRect into screenR
-- Set topleft:
put "3,40" into item 1 to 2 of screenR
-- Set right:
subtract 3 from item 3 of screenR
-- Set bottom:
subtract 3 from item 4 of screenR
-- Set window rect:
set the rect of window aWindowName to screenR
open window aWindowName