No, it is a major highway. Pedestrian traffic is are not allowed. Getting on the bridge as a group of people is very rare and requires significant critical mass to pull off.
The go-to location for major protests is the Taksim Square, which is four miles from the bridge by foot. The protests need to be really widespread and populous to spread to the bridge. I don't remember that happening in my recent memory (except for a local soccer thing).
