No.
It's been a dream of ours for some time. After all the Cisco CM can do a different user uploaded ringtone for every phone (Still can't do unique ring tones for different buttons)
Unfortunately Mitel phones will only let you change the pitch and volume of the warble tone.
Maybe, somewhere deeps in the bowels of the Contact Center software, there is a client that can do that.
I just haven't heard of it.
You may want to bounce that question in the applications section of the forum.
Ralph