Yes- you should be fine, but it won't cover any illnesses or problems already encountered. My daughter was travelling (not working) in China and the far east last year and had excellent insurance cover via STA travel and I have another daughter in Uganda at the moment who is insured through Endsleigh. Your son ought to be able to take the inurance out himself- online- if he has the means to pay for it online. If not, then as a parent I have phoned up and also gone on line to buy insurances on behalf of my adult children in the past with no concerns. I have found Endsleigh really helpful but I suspect other insurers are just as good. I haven't checked the opening times but they will often deal with enquiries quite late in the evening- you could call now!
isamatt