JDownloader is an opensource software, means you can inspect its source code to see whatever its infected or not.
However when you are installing it from a third party PPA, that means you have to trust the owner of that repository, because what you will download and install is already compile and packaged binary files which there is no way we can tell what it's going to do on your PC.
If the main program is some kind of malware so there is nothing you can do about it, if you install it you'll get infected.
Adware is some kind of software which show you advertise or changes and install some other advertising software on your system, Adware-free means it's not that kind of program.