If one installs Ubuntu 12.04, and does a distribution upgrade to Ubuntu 13.04, does the upgraded version still have five-year Long Term Support?
No, 13.04 is not LTS.
You cannot directly upgrade 12.04 to 13.04. You can upgrade 12.04 LTS to 12.10, and then upgrade 12.10 to 13.04. Both 12.10 and 13.04 are non-LTS.
Ubuntu non-LTS have historically been supported for 18 months. New non-LTS will be supported for 9 months. For example, 12.10 is supported until April 2014 (18 months since October 2012). 13.04 it is supported until January 2014 (9 months since April 2014).
Source: Releases - Ubuntu Wiki
About NKN's comment: note that upgrade has two distinct meanings:
- You can upgrade 12.04.* to 12.04.3, in the sense that you will have
up-to-date packages for the 12.04 series. This is done by
apt-get dist-upgrade(allows apt-get to install new dependencies if necessary) or
apt-get upgrade(does not allow apt-get to install new dependencies).
- You can upgrade 12.04.* to 12.10, so that you will have packages for the 12.10 series. This is done by
Simple answer: No.
By upgrading a LTS release to a non-LTS release we will have the support time scheduled for the upgraded release only. For 13.04 this will be support until January 2014.
We will however be able to upgrade 12.04 LTS to the next 14.04 LTS version after it was released in April 2014.