Daniel,
Short answer: Yes.
I have been previously and currently am involved with a few web app
projects that were started or rewritten from scratch on Drupal. In
fact, the reason that Drupal was chosen over any of the other CMS's
available is specifically because of its superiority amongst its peers
in the CMS space as a PHP development framework.
The most important thing in my experience is to make sure that you
approach the project from a correct perspective. You'll get the best
results if you think of the app being constructed *with* Drupal, doing
it the Drupal way. This is a very different thing than building it *on
top of* Drupal, where you try to reach down and leverage Drupal
functionality when it suits you. This approach might cause you to
rethink a lot of the application and data architecture in a rewrite.
Drupal can do the job wonderfully, but know that it probably won't just
be a "rewrite", but rather a "redesign", from the data model on up.
Allowing Drupal to handle all of your user management, for example,
sounds great, but thinking of how Drupal users are going to interact
with your application's data will force you to rethink how Drupal will
best do this. Ideally, it would become less and less your application's
data and more and more Drupal's content, structured in the way that
Drupal organizes its content (nodes, CCK, possibly OG's, ...), and
accessed the way that Drupal accesses content (Views, perms, ...)
...if that makes sense ;)
Seth