I suspect that for all realistic lifeforms, given travel at a few percent of lightspeed max, the ROI on interstellar travel (both on the financial and the individual-sacrifice-vs-benefit level) is so bad that you'll essentially only do it when your solar system is doomed.
And that takes you from exponential growth down to essentially zero growth.
There could easily be organisms that have lifespans in the thousands of years due to a variety of unique selective pressures (or no concept of a lifespan at all). Or species that have technology that can augment their lifespans to be thousands of years long. I can certainly see humans getting to that point in the next 10-thousand years.
Given a thousand year lifespan, what is a few hundred years in terms of commitment to a project? It would be something akin to working a job for 10 years or so, which is not entirely unheard of.
The ROI argument is more interesting! Although there are way too many factors to consider to have a definitive answer one way or another.
https://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia has been under construction for nearly 150 years; "construction passed the midpoint in 2010".
However as there would be no meaningful communication outside of a solar system, a single civilisation wouldn't spread to the stars
Don't forget to compare it with simulated annealing to find out if Skiena was right about GA in The Algorithm Design Manual when he said that he "[has] never seen any computational results reported using genetic algorithms that have favorably impressed [him]".