Yes, but there are so many other variables that play into survival. I agree the principle exists to an extent. Certain animals may be better suited to survive an unusual cold spell or change in environment.
But will that always strenghen the species? That I don't know. It might lead to extinction.
When I was about 4-5 I was with a group of kids playing Daniel Boone in the woods next door when my brother hatcheted a vine that just happened to be a yellow jacket nest. The older kids took off for the house yelling "bees" and I trailed behind. However the bees went after the fastest kids, slownest was a survival trait. I was stung less than anybody because I was younger and slower.
Apparently I was more fit than the older faster kids for an environment with bees that tend to attack the fastest kids.
Which illustrates the point about how many variables there are. Fitness for a "given environment" does not always lead to survival of the "best" specimens. There are senarios where natural selection can have a negative potentially devastating impact on a species. The protective behavior of herds may allow faulty genes to be replicated.
Then again perhaps it was randomness or providence that the bees went after the older kids. Survival of the Fittest is logical but is it even significant relative to luck or providence or other external environmental issues?
Even if it is significant, it's still doubtful in my mind that even given millions or billions of years, it would lead to the development of new functioning organs or transition between species, especially in those species whose gene pools are stabelized by male/female mating.