Does building a Docker image require the Docker daemon to be running?
Each command in the Dockerfile is processed as a separate step. Every step from the build process gets executed in a dedicated container. It starts from Step 1 (the first command in the Dockerfile). That step is run in a container and if it is successful, a commit to a temporary image (let's call it image A) takes place. Then, Step 2 is executed in a container which is run from image A ... and so on until the final step is executed successfully. And as Tensibai commented - how do you think to run a container without the daemon?

So, yes - building a docker image requires the docker daemon to be running.