some system binaries are lost After installing some RAM my macbook pro would not start,
diskutil showed HDD failure.

Booting in single user mode and running fsck several times to repair the disk lead to a running system.

But now, some of the Unix binaries (as well as some data) - like rm and less - are missing.
I have copied them from another mac.

The question is: if I reinstall OSX will it also install those and any other that might be missing?
If you mean doing an upgrade install from the recovery partition, it does replace many system files with the initial versions. It might not replace all files though, and for example setting or cache files might also be corrupted.

If you have backups, it won't take that long to try it out and see if there are still things that don't work. I'd just erase and reinstall OS X though.