Yea, he should be fine. He won't drown since RES are aquatic turtles and spend the majority of their life under water. They even sleep under water, only rising up for air every 10 to 20 minutes.
Give him 2 or 3 days of peace and quiet with as little commotion or human activity as possible. Then gradually approach his tank a little at a time for brief periods and maybe not too close so he can get used to seeing you but still feel safe and secure. Also he may not eat right away so try a pellet or two each day and see if he responds to them. If he doesn't seem interested after 5 or 10 minutes, take the pellets out and try again the next day. If he seems really nervous, you could even wait 2 or 3 days before feeding again. Make sure to leave him alone during that time.
Eventually he will realize that he is safe in his new home and will become more comfortable. He will also probably bask while no one's around. When he does become interested in eating, try to stay with him while he eats each time you feed him so he begins to associate you with food. Soon enough you will become his best friend.
