Multiple commits before pushing
Git is a distributed version control system. Your repository is entirely your own, and it contains absolutely everything you need. Committing takes place only within your repository; it has nothing to do with whether or not you're online.
The things that you need to be online for are pushing (publishing your commits to another repository) and pulling (fetching and merging commits from another repository). When you push, it will push exactly what you told it to - all of the commits on that branch. It doesn't matter when you made them or if your network cable was plugged in at the time.
All your commits will be pushed.