I would expect the enable pin to control both input and output (which are tri-state) so it should be possible to read as well as write to multiple displays. I haven't tried it with text LCDs but it's certainly the case with graphical LCDs.
Usually it's a status bit that is read from the LCD to see if its ready (however the current version of the LiquidCrystal library does not support this)
The memory mapping of character data is a little complicated in a text LCD and its probably easier to maintain a copy of sent characters in your sketch rather than try to read the character memory in the LCD.