Does favicon have any impact on SEO?

Google Calendar has just started changing it's favicon on a daily basis (relating to the date). I'd say it's a safe bet that if they're doing it then it has no influence on the SEO.

Favicon is for human recognition of a brand. A search engine has little reason to pay attention to that file. What concerns do you have about rotating that file in regards to how a search engine indexes and ranks your site?

The favicon CAN have an effect on SEO. I saw one case where a website had a favicon that was about 400kb in size - slowing the website down. Speed is a Google ranking factor and slow loading sites likely have poor metrics, which can also negatively affect SEO.

Also, most browsers automatically look for a file called favicon.ico in the root folder of a website - if the file doesn't exist a 404 Not Found error is returned - so it makes sense to have a small or blank file rather than nothing to prevent that extra server hog.

If you have a different favicon on each page, make sure to keep the file size as small as possible, to minimise the impact on download speeds.