Even the most fundamental Christian groups accept microevolution, inheritability of genetic mutation as you're describing it has, yes, been observed in repeatable scientific experiments. The real question is about whether this can be extrapolated to the origin of life.

A second question would be whether the accumulation of genetic mutation is of the character that gives rise to new biological systems (vertebral, vascular, pulmonary, nervous, auditory, optical...) or fundamental special shift. This question depends also on agreeing on an earth age, though. Even the most militant advocate of evolution would not claim much aggregative mutation in under 6,000 years.