Yes. Each rename (and any updates to content that happen at the same time) is just a new commit on the branch you do the edit on. It should produce identical history to doing the same operation via the command-line :)
On the command line, I can do multiple renames in a single commit/
If you want to do multiple renames in one commit then the command line is likely the best way.
Alternatively use this feature and squash them later when you have access to a terminal.
In that case you'd need to either force the next push because squashing rewrites history or use a separate branch to do the renames in the first place.
I think dfrey means that you have 10 commits, rather than just one.