Possibly, but there is no guarantee. Hair collected from a haircut often does not contain the hair follicle (root), which is the part needed for DNA extraction. Without the root attached, it is much less likely that enough usable DNA can be obtained for accurate testing.
For the best chance of success, we recommend submitting 25-50 hair strands with the follicle still attached. If available, sending an entire hairbrush can also be a very effective option, as long as it was used only by the person being tested to help prevent mixed or contaminated DNA samples.