Orbital period in itself is just a number. Interesting variable is how does the climate on planet change during it. On Earth climate gets affected because of axial tilt of the planet, giving different hemisphere different amount of solar energy during a year (due to length of a day and Sun path on the sky).

If those planets have little axial tilt and little variety in distance to their star, there should be little variety in climate on them.

Why not? Orbital period seems like the sort of thing life can evolve to adapt to relatively easily.

Sure, there would just be no seasons. Everyday would just be roughly the same temperature as every other day. If the orbit is very eccentric, maybe 3-4 days would be like a brisk fall day, and 3-4 days would be like a hot summer day, and the rest would all hover around that average.