As of WIX V3.9 the answer is a qualified "No" - Burn doesn't currently support dual-purpose per-user or per-machine MSI package.
A dual-purpose MSI package has the ALLUSERS property set to "2". When you build a WIX bootstrapper project referencing this type of MSI package you should see this type of warning:
2>D:\Robert\Documents\Visual Studio 2013\Projects\BurnTest\Bootstrapper\Bundle.wxs(18,0): warning LGHT1133: Bundles require a package to be either per-machine or per-user. The MSI 'D:\Robert\Documents\Visual Studio 2013\Projects\BurnTest\SetupProject\bin\Release\SetupProject.msi' ALLUSERS Property is set to '2' which may change from per-user to per-machine at install time. The Bundle will assume the package is per-machine and will not work correctly if that changes. If possible, remove the Property with Id='ALLUSERS' and use Package/@InstallScope attribute instead.
The build process for a WIX bootstrapper project will try and work out from the chained packages what type of burn installation to create (per-user or per-machine). The logic is convoluted because of the different places you can declare a preference for per-user or per-machine, and the potential conflicts between chained packages. But the general idea is the burn compiler will generate a per-machine installation, unless one of the chained packages is per-user, which will flip the burn installation into per-user mode. The key point is the decision to create a per-user or per-machine package is made at build time. To properly support dual-purpose MSI packages that decision would need to be moved to install time.