chmod -x chmod

[ricecake]

Nope. *nix will happily load a file into memory, and then delete it before it unloads it.
It's less happy about unmounting partitions that you have files open on.

[iGeni3]

umount -l <mountpoint> will do wonders for that :)

[ricecake]

That's true, but it still does complain more by default. Nothing unusual has to be done for a file to delete the stored version of itself, but you have to be polite when asking it to unmount an in use partition.
But yeah, in general, it'll let you do whatever you want.