This doesn't change the version of Access that runs the program. What it does is it tells whatever version of Access that Windows has associated with the .accde to open the database and PRETEND to be the Runtime engine. So you could have A2013 or O365 in control of the .accde - no way to tell. You need to look at the Windows file associations in order to determine what Application Windows will run in this scenario.
To control what program opens your application, you MUST use a shortcut that opens Access (whatever version) and passes in the name of the .accde you are trying to open. Otherwise, as Doc mentioned, you are at the mercy of Windows and the file association process and have no control over what app will actually run your database.
Multiple versions of Access will fight over who owns a particular extension. THAT is the major issue you run into since the last version of Access to open takes over the file association. I have no idea what happens if you try to open two different applications at the same time, each with a different version of Access but you should figure this out before committing to this plan. Once you have multiple versions of Access installed, YOU need to open Access and then open the app. You can no longer rely on the file association to always open the correct version.
The other major issue involves OLE automation. This issue you probably need to solve by switching from late binding to early binding so you pick the Office version at compile time rather than at run time.
It is bad enough when YOU, the developer, have to deal with multiple installed versions. I would never inflict this on a user willingly.
Newer versions of Access usually run applications created with older versions without issue. You always need to be careful about clean compiles but if you deliver .accde's then that is taken care of. That leaves you with the bitness incompatibility which is harder to deal with because that requires that you create the .accde's with the same bit version that will run the app.