Not natively (VS Code) or with GitLens (GitHub repo)
As you probably know (or written), there is a feature request
Right now, I know which lines are not staged (green for new, blue for edited) and maybe when I commit locally, highlight those lines in a different color (purple?) to represent “committed but unpublished.”
But for now, you need to switch to the version control part of VSCode to see what is about to be committed:

There you can inspect staged changes to be committed.
Note: there is an uncommittedColor, but I don’t know if it references staged or unstaged changes, or how it is used.
GitLens 6.2 does mention gitlens.gutterUncommittedForegroundColor themable color, but I don’t see it anymore in my current 8.3 GitLens version.
The Microsoft/vscode 60389 opened by the OP includes for now:
When you’re editing a file in Git, there are three versions of it:
- HEAD
- Index
- Working tree
So, there are two possible diffs to show:
HEAD <> IndexIndex <> Working TreeWe currently show gutter decorations for
Index <> Working Tree.
Since the file which is open in the editor is always Working Tree, it doesn’t make any sense to showHEAD <> Indexchanges in the gutter, since none of those two files is Working Tree.
Aug. 202&: Lefty adds in the comments:
In recent GitLens version its possible to temporarily enable this highlighting by pressing Ctrl+Shift+P and entering
gitlens.toggleFileChanges.It disappears on first edit though :(.