Not really.
The directory that serves as a common
repository for application-specific
data for the current roaming user.
AppData is, surprisingly, for application data, not for installation (Click Once/Silverlight applications aside). You can, and should still install into Program Files, just don't expect to write into that folder.
You can install software into AppData if you want it to follow a user about in an Active Directory environment, which happens if you put it in AppData\Roaming (the SpecialFolder.ApplicationData location).
You can also install into AppData if you want the software to be available to just the user that installs it. This can be useful if, for example, you have multiple users on the same machine, who all want to run different versions of the software in complete isolation.
If you want settings to only apply on the local machine then you use AppData\Local, which is SpecialFolders.LocalApplicationData - this will make AD administrators very happy as the roaming profile size won't suddenly jump up 50Mb or whatever the size of your software is.
If you wanted to create settings which apply to all users then you're looking at SpecialFolders.CommonApplicationData
You should remember never to rely on the actual name of the directory - localisation issues mean this can change and the location does change with OS versions two. You should be using the special folder enumeration in your software, or the equivalent in your installer.
Could you not install into Program Files, but use AppData as it's supposed to be used, and store your database in there?
It's to allow backward compatibility for programs that assume the old name but to also prevent programs recursing the tree and finding both copies.
Here's an article about this from Raymond Chen - I thought he did it on his blog, though, so maybe there's more there.
Best Answer
Program Files is for executables and other static files that came as part of the installation. ProgramData is for user-agnostic data generated during execution such as shared cache, shared databases, shared settings, shared preferences, etc. User-specific data goes in the AppData folder. Note that these are for non-user-visible data. User-visible data belongs in the documents folder (or music, video, custom sibling folder, etc.).
Please see Special Folders and Custom Folders for a detailed explanation. Note that the terminology used varies slightly between the name used in the documentation here, the name of the folder, and the name used by various enumerations used to get these paths from the system.