It's possible for the Texans to finish 11-5. If they do, they're probably in the playoffs. It's likely that the Texans are headed for something closer to 5-11, in which case they'll finish far out of playoff contention. The NFL playoffs have included 6 teams per conference since the 1990 season. Since then, the overwhelming majority of teams which have started 2-5 have not made the playoffs. But four have:
1990 Saints - 8-8, 2nd in NFC West, 6th seed, lost at Bears 16-6 in WC round
1995 Lions - 10-6, 2nd in NFC Central, 5th seed, lost at Eagles 58-37 in WC round
2002 Jets - 9-7, 1st in AFC East, 4th seed, defeated Colts at home 41-0 in WC round, lost at Raiders 30-10 in Div. Playoffs
2011 Broncos - 8-8, 1st in AFC West, 4th seed, defeated Steelers at home 29-23 (OT) in WC round, lost at Patriots 45-10 in Div. Playoffs