Interesting questions, and I believe the answer to both of them is no. As FumbleFingers points out, I can't establish this with certainty, but I will undertake to explain why I believe this is so.
I took some time to read over a number of passages that use the term evolutive. In the examples I have examined, the term refers in all cases (leaving out several which are direct translations of the Spanish evolutivo) to the study, science, idea, or application of evolution as distinct from evolution itself. So you could say that the term adds one level of abstraction to the term evolutionary. Here is one example:
Software systems are conceived by developers in an iterative, recursive, and evolutive way. 
This means that developers conceive of software in iterations (one pass, then another pass that goes a bit deeper, and so on), going back through to correct things as they go (recursive), and that the conception of the software evolves over time as the designer's understanding of the problem domain (the problem that your software is going to solve) deepens.
Among the methods of interpretation employed in practice and doctrine are the textual, autonomous, teleological, evolutive or dynamic, and historic...Under the evolutive or dynamic school, the international authorities interpret the Convention in light of the current societal circumstances, secondarily incorporating the intentions of the framers of the document, which were shaped by an earlier and different societal context (historic method). 
In other words, if you use the evolutive method of interpretation, you believe that the interpretation of the Convention evolves over time. If you use the historic method of interpretation, you believe that it (the interpretation of the Convention) does not. (Interestingly, there are analogous schools of thought in Constitutional Law, regarding how the U. S. Constitution ought to be interpreted.)
Now, it would be ok to substitute the word "evolutionary" in these passages, but the term isn't quite as precise: evolutionary can (and very often does) refer either to the science or study of evolution or to evolution itself. For example, here are two books:
Objective Knowledge: An Evolutionary Approach
Evolutionary Dynamics: Exploring the Interplay of Selection, Accident, Neutrality and Function
The first book is a series of essays arguing that objective knowledge evolves over time, so it is applying the idea of evolution to the idea of objective knowledge. It is obvious from context that it is not the approach that evolves, but objective knowledge. The second is a book about the dynamics of evolution.
Now, you could use the term "evolutive" in the first title (although it might sound a bit pretentious, since the meaning is obvious when you use the more common word), but the evidence suggests that it wouldn't be correct to use it in the second title since here the word is referring to evolution itself, or the dynamics thereof.
So, if you accept my assessment of the word's meaning, then the answer to your question is no, it is not a correct option. Your sentence is referring to a short period in terms of evolution itself, not in terms of the study, science, application, or idea of evolution. :)