Yes and yes.
May be not the few bytes changed, but a very little overflow. I'm talking about several MB to some GB files. First time they are seen, it will take hours to sync, both on upload and on download. The subsequent updates are much faster and roughly proportional to the data changed.
Also there is an indexed phase each time a big file is modified and before the upload begins. And there are big data areas that Dropbox uses on your hard drive.
Now... this is not something you want to have on your very small battery powered device.