Moving the binary location of MySQL for replication
Yes, you have two options.  Both require none of the data changes in any of the files during copying.


Completely shutdown the server you are going to clone.  Copy it over, make relevant .cnf changes (especially server-id), start up the new instance.
If you're using LVMs you can take an LVM snapshot while the server is running and then copy that snapshot over.


If you're doing this to get a slave running, in both cases you'll want to have run show master status before shutting down/taking the snapshot so you'll know what to CHANGE MASTER TO when spinning up the new slave.  I would recommend setting read_only=1, then check the position.  If going the snapshot route you can set read_only=0 so the master can continue to take writes.