Not necessarily, tbh. The Cards were 10.5 games out in late August. Since then they've been running on pure adrenaline and motivation. In the NLCS it seemed they ran out of gas because none of their pitchers could make it to the 6th inning.
Their bullpen beasted against a dangerous Brew-Crew lineup. Texas has better bats for sure, but I also wouldn't count on St. Louis' starting pitching to suck that bad for two straight series. If anything, they are well-rested. Also, winning last night ensured that Carp would be on the mound for Game 1.