Can I run on to treat a player while play is still going?

Yes, if you are qualified medical staff and the referee has given permission, under the SARU Protocol for Medical Personnel Entering the Field of Play:

• Permission: the referee must give qualified medical staff permission to enter. This can be given beforehand (for example in the change room) or by stopping play and calling the medics on. If it has not been given, clear it with the referee before kick-off; it may not be unreasonably withheld.
• While play continues you must not interfere with play or endanger players or yourself, must watch where play is, and must not go on when doing so would compromise play or safety.
• 10 metre guide: if play moves to within about 10 m of the injured player and medical staff, the referee should stop play. Assistant referees should alert an unsighted referee.

Apart from players and qualified medical staff, no one may enter the playing area unless they are BokSmart certified and have shown proof of it to the referee or assistant referees.