Is using the second terminal hole on the back of a switch electrically the same as bundling it with other neutral wires?
The two push-in terminals in those holes are directly connected, electrically continuous, or equipotential for a really high priced term.  Connecting the two neutrals to them would work just like the pigtail connection illustrated would. 
 There are a number of reasons NOT to use them though.  

Number one, the push in connections on receptacles and switches generally don't make a good connection, even though they are approved, legal, etc., they often cause problems, some minor, some major.  I never use them.  Ever.  (Now the push in connectors are not to be confused with the backwired connections that operate with a screw clamp - those are fine.)  

But you could use the screw terminals to achieve the same end;  the two neutral screw terminals and push in terminals are all connected.  This would again be legal and a good reliable connection.  

If this circuit is a multi-wire branch circuit that shares the neutral with two 15A or 20A circuits, there is a code issue using the screw terminals:  there's a rule that devices on those circuits must be wired in a manner such that removing the device does not open the neutral.  

This may be why the illustration is as it is:  pigtailing the neutral may not be required, but it never hurts.