No it does not - at least, not on the Pro plan that I use. Cloudflare Analytics is actually fairly limited in what you can see, and there is no download of stats.
In my dashboard I have the following. All graphs allow for daily or hourly 'points' and go back one month maximum.
- Requests Through Cloudflare - a graph of how many cached vs uncached requests occurred.
- Bandwidth - a graph of how much data was used (cached vs uncached) in megabytes or gigabytes.
- Unique Visitors - should be self-explanatory.
- Threats - a graph of 'malicious threats' split into Bad Browser, Human Challenged and Browser Challenged
- A map showing where threats have originated from.
- Top Traffic Origins - table with most popular countries.
- Top Crawlers/Bots - table of crawlers (e.g. Googlebot).
- Various pie charts of savings you've made using Cloudflare such as '90% fewer servers needed' or '80% bandwidth saved'.
It's interesting to look at occasionally, but I've never found it truly useful. If you need stats on specific files you may have to look elsewhere.