Base damage on your offhand weapon determines damage from your offhand hits so yes, it does matter although is it not all that much of your total dps.
No, it is not only the dexterity, combat rating, crit rating, hit rating and critical damage rating on the offhand weapon that make a difference.
Check vid if you want to know how to test it yourself.
https://youtu.be/oAGsdgJU0WI