Nice question, and i think yes, because survive, the offspring and alimentation are the most important topics of any living thing. Each organism have special strategies on that, feed, survive and mate (in general, reproduction) that makes them different and "unique" to another speces. All the organisms have obtained those skills through evolution, passing these traits that make them stand out and survive the environment in which they are adapted.
Everything in Biology without light of evolution have lack of sense, so understanding evolution and their influence for behavior, morphology etc. is really important. It's essential to know what, how and why shapes all living form on our planet. We can measure it through their fitness what reflect in their survival strategies.
A survival ability is an biological adaptation, yes? Adaptations are the products of evolution, yes? If yes, you may conclude that ... see above. Anyway the question is too general and an answer is evident.
Spreading genes is what really counts from the evolutionary point of view, and it's both survival as successful reproduction. If you look only at survival you may find that some animals do not maximize it. That can be puzzling if you do not take into account that they may maximize the fitness by increasing reproduction instead.
No, the animals don't need to understand evolution, in order to have functional survival strategies. ;-) They just survive, reproduce, inherit, vary, survive, reproduce, inherit, vary ... and that amounts to evolution by natural selection in the long run.
I'd agree with everyone else here, in that I think an understanding of evolution is certainly important. But it also depends a bit on the type of explanation you want to come up with for the survival strategies you study. I like Tinbergen's classification of the four complementary types of explanation you can produce for behaviours. There's a brief outline here:
In effect, he notes that when you ask "why does a species do that?" you can choose one or more of four types of answer, depending on how you interpret the question. You can choose to look at proximal explanations (focused on how an organisms' structure or behaviour works) or evolutionary ones (why the species evolved that way), and you can also split answers into dynamic ones (focusing on the history of change in the behaviour/structure) or static ones (looking only at the current state). Putting it all together gives a four-way classification of answers to these questions, in which each one may be ontogenetic, phylogenetic, mechanistic or adaptive...
Understanding evolution is clearly particularly important for some of these categories, but I'd go further and say that you can't really explain a trait (structural or behavioural) without considering all four of Tinbergen's types of explanation, which also requires some understanding of development and biomechanics...