With mechanical room ventilation is it necessary to have air supply in addition to extraction?
Is it completely necessary? No I don't think so.  As a comment pointed out, you are creating negative pressure.  This is good for sealing environments (ie: keep vapors from existing the room in a lab), or even help prevent fire from spreading via halls. 

However, you will notice some negative effects to.  For one, since the air will be pulled in through any cracks under doors and windows, if a door is not latched, it will likely be forcefully opened.  Depending on the pressure, this could potentially hurt a young child who is not expecting the door to be pulled open by the pressure when they turn the handle. Having a second fan push air into the room aleviates this by balancing the pressure.  It also reduces the strain on the extraction fan which may help it last longer.

Another benefit is that if one fan fails, you still have a second either pushing cool air in or sucking warm air out; it will function with reduced capacity, but it will certainly be better than no fan at all!

My guess is that you will need two smaller fans instead of one large fan, which might also simplify electrical requirements, installation and maintenance.