If I’m citing an entire play reprinted in an anthology, does it appear in italics?

Yes. As the MLA Handbook explains, the title of an independent work (that is, a work that usually stands alone, such as a play, novel, or artwork) is styled in italics, even when the work is contained in another independent work (27):

Shakespeare, William. Macbeth. The Riverside Shakespeare, edited by G. Blakemore Evans et al., vol. 2, Houghton Mifflin, 1974, pp. 1307-42.

The following example shows an entry for a work of art contained in a Web site:

Bearden, Romare. The Train. 1975. MOMA, www.moma.org/collection/works/65232?locale=en.