Suppose that $ Y $ is a scheme and $ f\colon X\to Y $ a covering of $ Y $ in some Grothendieck topology on the category of schemes (i.e. if $\{ U_i\to Y\}$ is a covering in the topological sense, then $ X = \coprod U_i$). Then we may consider the descent groupoid $\Gamma_0 = X$ and $ \Gamma_1 = X \times_{Y} X $ with source and target maps $ s,t\colon\Gamma_1 \rightrightarrows \Gamma_0$ given by the two projections (so for coverings in the topological sense, $ \Gamma_1 = \coprod U_i\cap U_j$).

It is natural to expect from a covering that $ Y $ can be recovered from $\Gamma_0$ by gluing along the intersections, i.e. $ Y =\mathrm{Coeq}( \Gamma_1 \rightrightarrows \Gamma_0 ) $. Equivalently, we would like the pullback square $$ \require{AMScd} \begin{CD} X\times_{Y} X @>{t}>> X\\ @V{s}VV @VV{f}V \\ X @>>{f}> Y \end{CD} $$ to be also a pushout square.

Do there exist sufficient conditions on a Grothendieck topology on schemes under which $Y$ is the pushout $$\displaystyle Y = \Gamma_0\coprod_{\Gamma_1} \Gamma_0 = X\coprod_{X\times_Y X} X$$ as above? Is this true for all the standard topologies (Zariski, etalé, fpqc, fppf)?