Yes that's lucky for them.
The Braves lost to the Cards by one game last year so they got lucky the rule wasn't there in 2011 avoiding a 1 game playoff. Then Braves come back and beat them 5 of 6 games this year and open a 6 game gap but the new rule sticks them in a one and done situation where one bad fielding game ends a 162 great season.
Yes we were also lucky to get them so much but if you subtract them from our record we still have 87 wins in 147 games for a .592 W% which would still keep us 2nd in the majors. And we would have one less win than the Cards even with their 15 extra games vs Houston.
If you drop the games with Houston for the Cards they have a 77-70 record that's a .524 W% or 13th best of 30 teams and put them behind the Dodgers who had a .531 and .526 without Houston.
So yes it helped them into the playoffs.
They play 6 games with the worst team in baseball by a mile since the start of Interleague, the last 3 times they made the NLCS they made the playoffs by 4.5 games total even with the 2nd Wild Cards, those other teams are getting much harder draws.
Look at the Dodgers getting stuck with 6 with the Angels going 2-4, so while they had 6 with a team better than the Cards even with a far much harder schedule. The Cards won 4 with the 90 loss Royals from the weakest division in baseball. The difference here is 2 games and 2 games is the difference in the standings even with the 9 less games the Dodgers got with Houston.
So yes it helped them into the playoffs.