Short answer is "yes"...longer answer is "it depends".
If you have basic scripts (i.e. copy a file, sleep, issue date commands, etc.), you're probably fine as-is. If you have anything performing more advanced stuff, you may want to check the MAN pages of the commands you're running via script, to see if the flag names changed (or are even applicable under Linux).
Your loops, if-then statements, etc., should be fine.