Can stretto occur during the exposition of a fugue?

Yes, stretto—the overlapping of a fugue subject with its answer—can occur during the exposition of a fugue.

While this technique is most commonly employed after the exposition to build toward a climax, it is not restricted to that section. An explicit example of this can be found in J.S. Bach's The Well-Tempered Clavier, Book 2, No. 3, where stretto occurs within the exposition.1