use inverse Wishart for variance in MCMC

When you have a posterior that looks like as one step in Gibber Sampler

$P(\xi | \Sigma_\xi, \theta) ∝ exp\{-1/2 \xi\Sigma_\xi^{-1}\xi\}P(data | \xi, \theta)$

Do you always assume inverse Wishart for $\Sigma_\xi$?

$\Sigma_\xi^{-1}$ ~ $Wishart(\nu_n, \Delta_n)$

where,

$\nu_n = \nu_o + N$, and $\Delta_n^{-1} = \Sigma\xi\xi^{-1} + \Delta_o^{-1}$

When I check the original derivation, it was for the case when the likelihood was in exponential family. Would this be true if $P(data | \xi, \theta)$ was an arbitrary function, not an exponential family?

I saw one author doing exactly this for a very complex likelihood function.