Yes, that is of course true.

When you go to open mode, you need to delete password storages, but after that when you enter your passwords once, they will be there until you flash again to closed mode.

Now as I think about it, I think it should be possible to back up your password storage in closed mode (using aegis) and restore it later on some day when you flash your device back to closed mode.
Same way when you are in open mode and have created your password storages, just before flashing to closed mode you could save your password storages for the day you will be flashing back to open mode.

Am I correct in the above, or is there something that prevents this in closed mode? (I know it works with open mode...)