Is it possible and reasonable to convert a complicated, heavily styled html page into an editable Drupal site page?
You can use drupal to develop and complexity of site including that of a complex css design.  I personally work for a digital agency and every single project I have been on has been built in drupal and has been heavily design oriented.  I have also built JS apps in drupal as well.

If you are looking for a theme out of the box then you probably wont find it as they are generally free and not a whole lot of design into them.  If you are comfortable or willing to learn to create your own theme and template files then you most certainly can do this inside drupal.

It all depends on your level of knowledge and effort.

Here are a few heavy sites designed in drupal:

http://www.elmwoodreclaimedtimber.com/virtual-showroom (js app, but the site is also built on drupal)

http://www.servicesource.com

http://www.jedunn.com

http://www.tnvacation.com/made-in-tennessee

With drupal you have CSS, PHP, and MYSQL which means you can do anything those technologies can.

EDIT***

Also to answer your question more specific it really depends on how much of the content will be editable.  Drupal provides a more flexible GUI type layout called panels and panelyzer that provides more of what you may need.  Research into Panopoly distribution as its geared more towards landing pages