Is it true in a presentable infinity category that algebras are homotopy colimits of free algebras?

Question

In 1-categorical algebra one knows that, in a locally presentable category, every algebra for a finite product theory is a colimit of free algebras. Is the same true for algebras of finite product theories in presentable $\infty$-categories? I would already be content to know this for $E_\infty$-algebras and modules over a fixed $E_\infty$-algebra in a presentable $\infty$-category. Thanks!