Answer
Yes.
Work Step by Step
$K_{sp}$ of $BaSO_4$: $1.1\dot{}10^{-10}$
$[Ba^{2+}]=0.0012\ M\dot{}48\ mL/(48\ mL+24\ mL)=0.0008\ M$
$[SO_4^{2-}]=1.0\dot{}10^{-6}\ M\dot{}24\ mL/(48\ mL+24\ mL)=3.33\dot{}10^{-7}\ M$
$Q = [Ba^{2+}]\dot{}[SO_4^{2-}]$
$Q=2.67\dot{}10^{-10}$
Since $Q>K_{sp}$, a precipitate will form.