Ma's Nordhaus–Gaddum conjecture for total-rainbow connection number

Let $G$ and $\overline{G}$ be complementary connected graphs with $n$ vertices. Ma's conjecture. There exist constants $C_1$ and $C_2$ such that

$$trc(G)+trc(\overline{G})\leq C_1n+C_2,$$

and this upper bound is tight. This asks for a tight linear Nordhaus–Gaddum-type upper bound for total-rainbow connection number; the source gives no resolution of the conjecture.