In a word, no.
While connected to an Express, most printers including the LaserJet M1132 MFP can only print - no other functions such as scanning or faxing will be available. Furthermore, if you need to print from an iOS device, you will need an AirPrint enabled printer, unless you want to connect the printer to another device that can act as a print server.
You should shop for an AirPrint printer. Start here: http://support.apple.com/kb/ht4356
Correct. To use AirPrint you need an AirPrint enabled printer. Check this link for a list of them:
There are ways to make your printer work, but not directly from the iPad or iPhone since it is not an AirPrint printer.