Yes in general.

See  Adámek and Rosicky, Locally Presentable and Accessible Categories Cambridge University Press, Cambridge, (1994).

T. 3.12 p. 143.

Of course "in general" I mean: every "algebraic theory" (many sorted) Set models. 

For topological algebraic structures, (like profinite groups) this equivalence isn't true for the  Yiftach Barnea example