Hi Diane
Unless your son's elderly Uncle claims AA or DLA middle care or daily living component of PIP then the answer is no, your son would not be able to claim SDP.
SDP is usually only paid to single claimants living on their own in receipt of AA/PIP daily living/DLA middle care unless the person they are living with also receives to one of the above benefits.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems