I would like to reproduce the way Vagrant logs in to my VM within a shell script using an ssh command, so I create an alias to my Vagrant instance.
What
Just pass the entire vagrant ssh-config as a config file to ssh with the -F configfile parameter. The host alias to connect to is defined on the first line in vagrant ssh-config; Host default means you can connect with ssh default.
I couldn't see an option to read the config file from the standard input, so went with the temp file route. Here's a one-liner that also cleans up the temporary $TMPDIR.vagrant-ssh-config file afterwards. It needs to be executed in the same directory as your Vagrantfile, assuming you vagrant box is up and running.
vagrant ssh-config > $TMPDIR.vagrant-ssh-config && ssh default -F $TMPDIR.vagrant-ssh-config ; rm $TMPDIR.vagrant-ssh-config
Note: on my Mac OSX system, $TMPDIR expands to /var/folders/46/yltlhtgx8m5cg68_w95wgvy41324gn/T/ (right now). Use another variable, or another folder, if it's not set on your system.