If you are talking about the "display" part of the dropdown (the part with
the currently-selected value, if any, and the dropdown button), then
changing its size on focus would be a horrible UI behavior.
If you are talking about changing the width and/or height of the dropdown
LIST, then that's another matter entirely and I think it would be a
wonderful UI choice, because there's nothing worse than trying to choose an
item from a dropdown list when you can't see its entire text, especially
when there are others with similar text at the beginning.
By the way, what are you talking about? Web? Windows Forms? WPF? Kinda
important....