Question

I have the assumption there is no added protection at all.

Answer 1

There is no difference in the security provided, but because of the way compression algorithms work, you are probably going to get better compression if you compress first then encrypt.

Compression algorithms exploit statistical redundancies (such as those that exist in natural language or in many file formats) in the data which should be eliminated when you encrypt it, therefore an encrypted message shouldn’t be able to be compressed all that well.

From the wikipedia article:

However, lossless data compression algorithms will always fail to compress some files; indeed, any compression algorithm will necessarily fail to compress any data containing no discernible patterns. Attempts to compress data that has been compressed already will therefore usually result in an expansion, as will attempts to compress all but the most trivially encrypted data.