Yes, this is possible. You can create a setup.exe bootstrapper to install thinks like the .NET Framework of C++ redistributables and then launch your MSI. In your MSI you can use the Setup Files (SUPPORTDIR) pattern to have a temp directory with a bunch of resources and invoke an EXE in there. When the EXE closes the installer resumes, cleans up the temp directory and exits without ever technically installing.
Crazy idea? Perhaps. But Team Viewer optionally uses this approach and it works very well. Some people get a meeting invite and really don't want to have to install yet another screen sharing program.