Question: Can the Fell topology be expressed in terms of the distributions of the the tracial states of a unitary representations, that, is $\pi_j \rightarrow \pi$ if and only if $tr\; \pi_j \rightarrow tr\;\pi$?

This makes of course only sense in a more restricted setting, say reductive groups over a local field $F$. Otherwise, it isn't clear whether irreducible unitary reps have tracial states.

Examples: This is true for $GL(n,F_v)$ for $F_v$ local field and $n=1,2$. Also works well for $SL(2, \mathbb{R})$.