In short, yes it can.
Your hair has three stages of growing; active growth, transition and finally a resting phase. About 85% of your hair is in the growing phase at any one time with the rest in transition or resting. An increase in stress – from a physical injury or emotional problem – can make more hairs suddenly enter the resting stage. It’s a way for your body to focus on the more important problems you may be having.
This stress-related type of hair loss happens about three months after the stressful event, so you might not make a connection between the two things. The good news is the hair will regrow once the stress levels have dropped. This very often happens to pregnant women about three months after having the baby. The drop in hormones after having the baby sends the hairs into resting period, and then three months later a larger than normal number of hairs all fall out together.
Different hair cells across your body have different maximum times of growth which also explains why the hair on your arms, and…er…other bits, will never grow long enough to put in an impressive French plait. Hair grows about 15 centimetres a year and most people have a growth time of 30-45 days for the hair on their arms and legs, meaning that however thick and bushy it may seem, it probably won’t grow much beyond a centimetre in length. This difference in growth time is also why some people can grow their hair very long and others struggle to get it past shoulder length.