Probably not, but I applaud Mayor Jim Schmitt for trying . I understand the appeal of Los Angeles, but it's currently not an NFL city. I don't know if the league would factor that in, but it should. The draft takes place in late April/early May, so weather isn't an issue but hotel space likely would be. I believe the teams history and Lambeau field do make it something the league would at least have to think about.
The draft itself likely would be held at the Resch, right next door to Lambeau Field. Lambeau itself could likely be used for periphery events. I think it's a long shot but I see no harm in Schmitt trying.
Photo credit: By YF12s at en.wikipedia [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], from Wikimedia Commons