After the files are analyzed the replay gain values are kept as metadata in the library and in the physical file tags when possible. During playback MC uses the values for adjusting the playback volume if Volume Leveling is enabled. The audio content is never altered.
The album gain value is calculated dynamically. To make it appear the album needs to be detected as complete (check the program help for info about the complete album logic). The album gain value is used during playback if enabled in the Volume Leveling options.
Some hardware devices are able to read and use the Replay Gain tags, but I don't know if your Alpine can do that. So far I have not stumbled on a car player that can do it.
If you want to adjust the files permanently so that they will play at equal volume levels on every player you can use the MP3Gain program for adjusting the audio content inside the files:
http://mp3gain.sourceforge.net/A good option is to first adjust the files by using the Album Gain option in Mp3Gain (this will keep the files inside each album at correct relative volume levels) and then analyze (or reanalyze) the files in MC so that you can use the track gain option during playback when preferred.
If MC has old replay gain values you need to reanalyze the files after they have been altered with MP3Gain.