If one boots a live session, does an update to the live session and then create a usb boot drive, would it contain the updates?
2 Answers
Your question is too brief, please be more specific.
Do you mean already having USB live media with an overlay filesystem (to install updates and also keep files and settings) and installing (via ubiquity installer) from that updated USB live media to another drive that can be connected via SATA, eSATA, USB, etcetera?
Package cache on live media with overlay filesystem
In theory, if the location for cached packages is the same for the installer as it is for the live media's package manager and regular installations (where it is /var/cache/apt/archives/
) and still contains up to date packages, then packages should be fetched from that directory instead of being downloaded again. You have to enable the option to download and install updates during installation, of course. As I said, this is a theory, one has to verify this behavior first.
Using the package cache on the fresh installation
Alternatively you could copy the updated packages you already downloaded to /var/cache/apt/archives/
on the fresh installation and run the update manager (or use apt-get
to see what will be updated and what will or is being downloaded).
Alternatives

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It is doable. You will need UNetBootin for this. It utilizes overlay-FS to make changes persist. Running the program will give you something similar to this screenshot
Select the radio button labeled "Diskimage" (1), then the button labeled "..." (2) to select the .iso image from your local filesystem. Now type in the size of the overlay-FS that will be available to your system in the textbox (red square).
We are almost there. All that's left to do is select the USB device from the drop-down labeled "Drive" and hit the button labeled "Εντάξει" in my screenshot.