I don't think this is quite there. A UTM is itself a TM, and its transition function is fixed. But it emulates a TM, and it could instead emulate a TM-with-variable-transition-function, and that thing would be self-modifying in a deeper sense than an emulation of a standard TM.

But it's still not obvious to me how to formalize this, because (among other problems) you can replace an emulated TMWVTF with an emulated UTM which in turn emulates a TMWVTF...