SSIS 2012 Ftp parallel/asynchronous multiple file download
Native, no. 

Heck, I barely classify the out of the box FTP component as a real component. It meets some technical specification for FTP only for the most rudimentary operations. I've usually gone the route of calling ftp.exe from the Execute Process Task with a parameter file or just used the .NET libraries for doing so.

I had never thought about parallelizing FTP downloads but this question over on SO looks like a valid implementation of it https://stackoverflow.com/questions/18117536/c-sharp-multiple-download-from-ftp-using-parallel-task-duplicate-download-issu

Depending on how you design things, I've come to the conclusion that having packages download files and then perform operations on the file(s) it might have found is a painful pattern. Instead, I find I've had better results with separating those activities and making an assumption that the consuming package will only run if data already exists. This allowed me to make radical changes to how I acquired the data (we went from SFTP to FTP with no core package change) without having to validate/retest the processing of the data. Might not be an issue for me but simplified my compliance life.

The net result of the above was that my agent job went from "run Package" to "run ftp package", "test for existence", "run processing package" or "alert that no file found". Modularization allowed us more flexibility as well as letting more people work on the problem vs one person working on a monolithic package.