Translating SAT to HornSAT
No.  Conjunctions of Horn clauses admit least Herbrand models, which disjunctions of positive literals don't.  Cf. Lloyd, 1987, Foundations of Logic Programming.

Least Herbrand models have the property that they are in the intersections of all satisfiers.  The Herbrand models for $(a \lor b)$ are $\{\{a\}, \{b\}, \{a,b\}\}$, which doesn't contain its intersection, so as arnab says, $(a \lor b)$ is an example of a formula which can't be expressed as a conjunction of Horn clauses.

Incorrect answer overwritten