Typically, there are three reasons I have come across frequently as to why the Additional Content does not correctly download.
1) The ISP limits the size of any single contiguous file and so the Additional download 'breaks' when it reaches this limit... causing the complete download not to properly complete.
2) Permissions /account errors... usually caused by the User having used Migration Assistant or Time Machine to move data over to a new computer in the past....
3) The computer goes to sleep during the downlaod process causing an abrupt termination of the download...
The third one is actually the most common and is easily fixed by going to your Energy settings and making sure that both screen and computer are set to NEVER sleep and also make sure you uncheck the "Put HDs to sleep" option... You can put these back to normal settings afterwards.
The second option is fairly common and there is no easy way around this other than try and repair permissions to resolve the issue and if not, to do a fresh install of OS X and then Logic... I have tried using BatchCHMod on occasion to fix this and sometimes it does but other times it causes more issues than it fixes... when used improperly. Here is a link to my 'Method' of installing OS X and Logic from scratch that seems to work in most instances... be warned.. It is a time consuming method though and there are no guarantees of course.
https://discussions.apple.com/thread/4142085?answerId=21140172022#21140172022
The first possibility is something I have come across several times but it's not that common... A Call to the ISP in question, asking them to remove this max file size limit, often resolves this (if they do indeed have such a limitation in effect for your account) but you may need to get through to the right tech support person in order for them to understand and be able to change this setting on your account.
Finally, I can tell you I have personally installed several Logic Pros with Additional content in both Lion and Mountain Lion, without any issues whatsoever.... so yes, it can and does work.