Bidirectional Vagrant Rsync

Unfortunately no, quote from documentation:

The rsync synced folder does a one-time one-way sync from the machine running to the machine being started by Vagrant.

so better for you to use NFS (or SMB if using a Windows host)

In some cases the default shared folder implementations (such as VirtualBox shared folders) have high performance penalties. If you're seeing less than ideal performance with synced folders,

Consider using a vagrant plugin https://github.com/smerrill/vagrant-rsync-back#vagrant-rsync-back

Install:

vagrant plugin install vagrant-rsync-back

Run:

vagrant rsync-back

It'll rsync the mapped folders from guest to host