It kinda depends on the variety of poppy you're raising. All various varieties can be deadheaded, but keep in mind that two of the varieties are actually annuals (the Icelandic or Armenian and the California) and reproduce (profusely) from self seeding. All, as stated, benefit and prolong their mid-summer season a little bit by deadheading, but be sure to leave some to go to seed. Many gardeners collect some of the tiny black seeds to plant elsewhere or give to friends.
The pervasive Oriental poppy dies back soon after blooms fade and that's fairly early in the season, so one needs another "late bloomer' to help cover the area...