Multiple server FTP download class
Overall - looks good and readable. Just a few comments.


I didn't quite get it but looks like you are relying on exception to be thrown to get a signal and download file - this is bad and expensive.
Is there a way to check if this is file and download instead of trying to treat it as directory - cwd - and catch exception.
Is this what you are trying to do?


In general it is bad to organize program workflow around exceptions - they are for exceptional situations - not for routine work.


Use os.path.join to concatenate paths - link
Use some constant like ROOT_PATH instead of hard-coding '/'
Use logging module for debug/error logging - this is industry standard
Don't swallow exceptions - log them, use extended except:

except Exception as e:
Minor - use "{0}{1}/{2}".format(host, current, file) instead of % notation as this is sometimes wonky and format is just better and industry standard.
Small comment - you are hard-coding logic on where to download files on local disk inside Ftp class which is working but not the best - just add optional parameter to be able to override root directory where to download data to.