Mandrake used to be advertised 99.999% compatible with RedHat. It was originally a branch off RedHat. So, yes, it is built on RPM packages, and you can use them to install new software.
Now, as to whether you can use just any RPMs with Mandrake, the answer is no. You need packages that are built for the version of Mandrake you are running. Same is true with RedHat, SuSE, and the others.