Are cookie read/write atomic in browser

I am trying to implement a cross tab mutex for my needs. I found a implementation here. which seems quite promising. Basically, it implements Leslie Lamport's algorithm with needs atomic read/writes for creating a mutex.

However it relies on localStorage providing atomic read/writes. This works well in most browsers except for Chrome.

So my question is, can I use cookie read/write instead? Are cookie reads/writes atomic in all mainstream browsers (IE, Chrome, Safari, Firefox)?