Let $C$ be an $(\infty,1)$-topos. The $(\infty,1)$-category of group objects in $C$ is a full sub-$(\infty,1)$-category of groupoid objects in $C$: $${\mathsf{Grp}}(C) \hookrightarrow {\mathsf{Grpd}}(C)$$

Is this full subcategory reflective? Here is one way to go about constructing a $(\infty,1)$-functor in the other direction: $${\mathsf{Grpd}}(C)\xrightarrow{{\mathbf{B}}} C \xrightarrow{R} {\mathsf{PointedConnected}}(C)\xrightarrow{\Omega} {\mathsf{Grp}}(C)$$ The functor $R: C\to {\mathsf{PointedConnected}}(C)$ takes an ordinary object $X$ in $C$ and gives its pointed-connected-reflection, given, say, by taking the homotopy cofiber of the inclusion from the 0-truncation $X_0$ to $X$. Conjecturally, the above $(\infty,1)$-functor could be the group reflection of a groupoid object, but it's really a guess.

So, the question: is ${\mathsf{Grp}}(C)$ reflective in ${\mathsf{Grpd}}(C)$? How can we give the adjoint?