Can I get iOS notifications for emails routed to folders?
There is not a native way to do this in iOS, but there are many possibilities for workarounds. Here's one:


Set up Boxcar and install the helper app on your iDevice.
Create a rule in Boxcar telling the helper app to get a push notification every time a message is received at the forwarding address provided. If you need help with this, see this help article.
Create a rule (or whatever they're called in your email service) which automatically forwards folders' new messages to the Boxcar address.


If this fix doesn't suit you, you may want to do a similar thing with ifttt.