Could Hermione really free Hogwarts' House Elves?

In Order of the Phoenix, do you think Hermione could really set House Elves free just by having them pick up hats and socks? I have serious doubts that her plot to free the house elves would actually free any of them.

1) The students are not the Master of any of the elves. That would be Dumbledore (or whoever the Headmaster is). So it seems to me that only Dumbledore could set them free.

2) I don't consider "being presented with clothes" the same as "picking up an article of clothing". If all it took to free a house elf is it picking up a random article of clothing off the floor, then there really wouldn't be any enslaved house elves. I'm sure, for example, that the laws that govern house elf ownership make specific exemptions for doing laundry. (I giggle a little every time I try to picture Lucius Malfoy, for example, attempting to wash his own socks.)

Hermione's heart was in the right place, but I wonder about her planning here. It just doesn't seem like it would be as simple as she tries to make it.