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[eluser]jwindhorst[/eluser]
Given that scenario, I suppose it could cause some problems, but:
A) I find it suspect to assume that your domain doesn't have it's own document_root at /mydomain/app/
and
B) You should be able to adjust for that by making a change to your config like below:

Code:

if($_SERVER['HTTP_HOST'] == "sharedserver.com")
  $config['base_url'] = "http://sharedserver.com/app/";
else
  $config['base_url'] = "http://dedicatedserver.com/";

Granted, you've made your point and without testing it this is just theory, but I do think something like the above would fix the problem your describing dynamically upon moving the code.