Can't see why you should not be able to dye it ... after all, it is cotton.
Yup, I agree ... just bite the bullet and go for it and find out.
First though, you could Google ... I just did and as expected a huge amount of info awaiting.
Plus found places that do the specialty dyeing, in case you are not really wanting to do it.
However, there is nothing like DIY and being able to say
♪♪I did it myyyyyyyy way♪♪
(just to quote Frank Sinatra!