Sure he could. So could Clinton. The only reason why either candidate gets a briefing is because every sitting president since Truman has ordered it. If the president ends it then he ends it. But he isn't going to. For either one.
I hope Trump has some smart, experienced intel advisors who know the ‘business’ and how to interpret what they’re being told, as well as what is not being told. The intel community is under political pressures to shade things certain ways. He needs to let them know he might be their boss, and will hold them accountable.