Does the altered files of dmg folder with a password protection get saved from a time machine backup?

Alright so i have several dmg folders that i've installed password protection on, inside these folder are obviously sensitive information - as someone who regularly backs up my files i wondered if i added more documents to these password protected dmg would time machine back them up? When i entered time machine to test this i clicked on the dmg folder but they wouldn't open or even give me the option to enter my password at all instead all that pop up was a short information about the file like size etc - so my question is does time machine back up any newly added files to a dmg folder with a password protection added on?