> would an embedded device also come with a 80 GB hard drive
Just about any would, over e.g. NFS or samba.
Additionally, some wireless or wired routers also have USB capability that you might use for an external storage device (not tried, but seems plausible).
> have regular security updates for its firmware
That's pretty much guaranteed if you're running a mainstream alternate firmware, e.g. dd-wrt or openwrt.
It's a good reason to use alternate firmware, besides the better features.