There would still be mutations, and in a few generations you would end up with a population carrying possibly dangerous defects. Given the small starting number, a large fraction of them could carry it.
Also, they're going to bring a bunch of microorganisms with them that are going to continue to evolve. Genetic diversity is absolutely necessary for large organisms to adapt to the evolution of smaller ones, that's why nearly everything that's big enough to be seen by the naked eye has some form of sex.
The best solution, I insist, would be an all female crew and a few gallons of frozen sperm. In the beginning, you would use artificial insemination to keep genetic diversity high. The all female crew would be there to ensure high fertility, and get the fastest possible population growth. Once the population gets large enough, as each potential mother is less critical, you can reintroduce males, while still using frozen sperm to increase the genetic pool.
Normal breeding should be allowed only when the population is significantly larger than the minimum requirements for survival. 1% children with genetic defects might not endanger the group, but if waiting for another generation allows this number to drop to .1%, it would be criminal not to do it.
If there is no answer, there is no question. If there is no solution, there is no problem.
Waffles to space = 100% pure WIN.