Last tested: Jan 21, 2019
No, in order to submit a pull request via the Looker UI, that user must have their own remote git account.
More context: We built a git development environment that separates commits by Looker users. We haven't built out pull requests for this environment, so we use the implementation of the Git service (ie Github), which means you need login credentials to that service.
This content is subject to limited support.