Does Time Machine back up potentially corrupted files? I have an external hard drive that I bought for my laptop so I could back up the important stuff and do a clean install, as somehow I got that stupid MacCleaner adware thing on it and it was causing issues.  

I've used Time Machine only back then, several months ago.  After doing a clean install, low an behold, someone's contact info directed me to update Adobe Acrobat and then quickly scrolled through some boxes where I accidentally clicked on something to install something similar (doh!).  I followed the instructions to get it off my laptop but I'm not sure it's all fully gone as I occasionally get some pop-ups.  

Question, now that I'm backing up onto external drive again using Time Machine, will those little bad files also be backed up as well, or does Time Machine just back up files and applications?
Time Machine cannot know which files you consider "bad" or "good". Thus Time Machine backs up both classes of files just the same.