Yes a hand blender will work to whisk eggs with and if you have a hand electric blender with the attachments you can use the mixing attachment without the blender to whisk eggs by hand with.
When you whisk you just move the whisker around in a circular motion instead of just spinning it around in the eggs.
But you can whisk the eggs up also if you want to by turning the mixer on and doing it that way.
I would recommend buying a cheap hand whisk as well as they are handy to have and are cheap to buy.
But mixing the eggs up with a hand mixer will give you near the same results as whisking the eggs by hand as you're mixing the eggs and introducing air into the eggs as well.