It'll "work", but you stil need to connect the diodes to the switch terminals which will add connections - typical handwires use the diode legs as part of the matrix, which would still sit below the switches. In short, you can do it but I don't think you'll get the benefits you're looking for and you'll be adding complications and potentially more soldered connections. The diodes aren't the things that add any real thickness to the board.
I've seen people squeeze out a mm or two by bending the switch pins, alternatively you could look into the low pro switches.
