From the Audacity manual we can read that it will not build against FFmpeg libraries newer than 0.8:
Audacity should support building against FFmpeg 0.5 through 0.8. It may not currently be possible to build Audacity against later versions of FFmpeg.Audacity Manual
From 14.04 we will have installed libavcodec54 by default. This will conflict with older libavcodec releases. Audacity is already compiled and built against libavcodec and LAME:
Some Linux distributions (for example, Ubuntu) now package Audacity with MP3 encoding and FFmpeg support already linked dynamically to the relevant system libraries. In these packaged builds there is no need to locate LAME or FFmpeg, so Audacity will have no "Libraries" Preferences.Audacity Manual
As it appears to be possible to still compile Audacity with newer FFmpeg releases for file format conversions not natively supported by Audacity.
If we only need to export to a non supported file format it may be easier to just use Audacity's option to export using an external application. This unfortunatley is not implemented for file import.
On the export file format dialog we can choose (external program)
instead of an inbuilt format. On Options...
we can then define a pipe to any external converter including avconv which had replaced FFmpeg.
avconv -i - "%f"
The output format will then be determined by the file extension given.