All that git stash does is make a commit. (Well, two commits, but that doesn't matter just at this point. The commits git stash makes are on no branch, and are structured oddly, but the key is that it makes commits. That's because commits are the way to save files in Git. Even Git's git notes are commits! Like stashes, they are not on branches, but they do save files, so they are commits.)
If you can make a commit with git stash, you can make a commit with git commit.
If not—if you have not completed the resolution of the merge conflicts—you are basically stuck. You must resolve all the conflicts before you can commit. See How can I save a git "rebase in progress"? for (much) more about this.
Note that if you have a new enough Git to have git worktree add, you can set up multiple work-trees, each on a different branch. Each work-tree gets its own index (see that other question and answer for why this is important), so it's possible to leave an in-progress rebase with merge conflicts in "the" index and switch to another branch in another work-tree and do ordinary work. In other words, "the" index is now a per-work-tree index, so the fact that the merge conflicts are in "the" index "locks up" that one work-tree, but not any others.