I received a reply from Rogers Redding. Here is the reply along with my question:
Can you clarify the rule for a player who is injured. I understand the rule does not allow a player to "buy" himself back into the game with a team timeout. If the injury occurs and then the period or half ends, will that player be allowed to come back for the next play? I know that for the helmet coming off rule, 1 play means 1 play so I am just curious if the injury rule is different.
"The player must remain out for the next down, regardless of when that is."