[dfacer]

Can I put Hardie Backer right over the drywall and then tile?

[joypulv]

It depends..
Is the tub or shower base in place and will the thickness of the wall now be too far out over the edge? If so I would remove the drywall. (Note that 1/4" backboard is not sufficient to keep tile from cracking if someone leans on it. Note that Hardie board has wood fiber in it and needs 1/8" expansion gaps.)
If you can keep the drywall, put up a vapor barrier to keep mold out of water gets through the grout over time, and to keep any steel fasteners from rusting and popping.

[smoothy]

You COULD do it but it might look like hell because of the additional thickness of the hardyboard on top of the thinset and tile. There aren't a lot of situations that come to mind where that thickness won't be important.

Is there a reason for not taking the time to remove that section of sheetrock?

[massplumber2008]

In my opinion, the correct answer is NO, you should not install cement board over drywall.

Simply put, the existing drywall should be removed, the stud walls should be inspected (probably some nasty/moldy insulation behind the wall), and the cement board needs to be installed properly.

Mark