(Disclamer : I'm one of the main developers of git-tfs...)
I've tried using GIT TF and it works using checkin --deep. (not working with branches though)
Is this somehow possible using GIT-TFS?
Perhaps, if you know perfectly well how git-tfs works, you could end up with what you ask for (because git-tfs support branches). But it won't be an automatic process, you will have to do a LOT of things manually (with hours and hours of hard work to do!). I highly recommend against trying to do that. The way Git works and TFS works made it very difficult to migrate from Git to TFSVC...
Git-tfs was created to use git locally when you are obliged to use TFS as source control or to migrate sources away of TFSVC because that's not a good Version Control System.
Don't try to use it to be locked using TFSVC :(
I think that you should better either migrate your sources inside a Git project in TFS if you have TFS2013 or use Git as central repository.