Basically, you can use cp wherever you use dd, as long as you're not changing any low-level parameters (e.g. starting 500 bytes into the file or something).
Yes. Yes it does. Reminds me of a Sunday evening in the late 90ies when I stopped working as root all the time:
cp backup.tar.bz /dev/sda
Nowadays I would know enough to at least get the contents of the backup.tar.bz back. Back then, this was the end of both my / partition (or any other partition) and the backup of my music collection.
Still, that didn't end my love affair with Unix. It did make me a whole lot more careful though.
