Yes, transplanted hair can go grey, just like all your other hair. The transplanted hair comes from the donor area, typically where hair is more resistant to hair loss. So, it still retains the characteristics of your natural hair, including its potential to grey over time.
The primary goal of a hair loss treatment is to restore hair density and coverage, not to alter the natural colour progression of your hair. Hair transplant procedures don’t stop the natural ageing process. So, as you continue to age, the hair growth from the transplanted follicles may eventually turn grey.
However, it is important to note that transplanted hair is perfectly fine to dye after a few weeks. This means you can colour your transplanted hair the same way you would your native hair.