This will be rushed. Please tell me what is not clear.
Custom Action: In order to implement exactly what you describe, you generally need a custom action. This is always unfortunate since they are very error prone: Why is it a good idea to limit the use of custom actions in my WiX / MSI setups?
Alternative?: If you ask me I would install the database in a component of its own, make the file the key file and set the component to permanent and never overwrite if key path exists.
In the WiX source: for the WiX component element, set these attributes: Permanent="yes" NeverOverwrite="yes"). I am not 100% sure what will happen if you do something stupid such as setting REINSTALLMODE="amus" during installation (force overwrite all files regardless of version). It has been a while since I tested the NeverOverwrite flag. But for normal deployment done the regular way the database file should be left alone and not overwritten.
Custom Action Overview: There are properties called Time and Date that are automatically set in the installer, but the Date property will generally contain characters that are illegal in path names. It is possible to just get the properties and replace the illegal characters. However, the date separation characters are probably different based on regional settings and hence hard to predict. Your code could get messy quickly and testing would be challenging (potentially many locales to test depending on distribution scope - a truly globally capable package is challenging).
I would rather get the date and time some other way - via some programming API call where I can determine what format the data comes back in. You also need to run this custom action elevated in deferred mode to ensure it doesn't fall over with access denied (insufficient user rights for operation). This is always quite a bit of clunk to set up and get working. Maybe try the alternative approach first?
I have long considered adding a custom action to abort the install if REINSTALLMODE="amus" has been specified. I would prefer that and the alternative approach described with "never overwrite" to a custom action doing all this copying.
