Will Ubuntu 14.04 Trusty Tahr request me to update when the actual LST gets released or will I have to manually download another image file and install on virtualbox?
Of course it will.
If you would have changed your repos on a 13.10 machine to
Trusty ones, it would have went through all the alpha and beta phases. And finally changed into the final one.
Versions are basically meaningless. They only state milestones. Alpha, beta, RC tags too.
Big versions (such as 13.10, 14.04, LTS) only mean LTS/stable states, and that's it.
Even LTS/stable is just a different support timeframe nowadays.
(In the past, LTS had no major upgrades. I mean, in a Debian kind of way.
But that's not true anymore, even the latest LTS had a major graphical stack change lately.)
Even more explanation...
In Debian, you can stay on channels for testing, still-in-development and experimental, without ever rewriting your sources.list, or changing anything. Well, indeed, you need one change after a clean install. But that's it.
Ubuntu does not have this... yet. There is only a development channel by the new codename (which was Trusty Tahr). Which meant a highly unstable - usable - stable states altogether. It changed as time passed. Again, things can go FUBAR even with the latest beta.
With LTS versions (well, branches/codenames), you can usually switch to the new channel sooner, as LTS gets imported from Debian's Testing tree. Not from SID. But this is not a rule, you just have a better chance of getting a working system. If the state of testing is in a bad shape, things won't look any better.