I know soffits are dated looking, but I don't really want to mess with opening up walls, structural work, etc., when I update my kitchen. Do you think that will hurt me if I decide to sell down the road? and if it woudl, is it a do-it-yourself job?

Normally soffits are easy to remove but before you do make sure they are not hiding items such as ductwork or plumbing. Soffits also give a dated look and by eliminating them your kitchen will feel and look larger. I haven't seen soffits specified on kitchen plans for at least the last 15 years. Take them out if you can.

Will knocking on the soffit and listening for a hollow sound be enough to tell what's behind it? Is there any way to be sure that there's nothing critical there before opening up the wall?

No. If this is a one-story home that has an accessable attic above, you can crawl up there and look down into them. If you can't view them from above, you can make a series of "peep-holes" in the face of the soffits so you can actually see what is inside.