When you say 'connect', what do you mean? ssh? You could probably write a bash script to accomplish this, and have the script executed in your .bashrc or .bash_profile file. You will have to learn a lot about Xorg too. Your script would have to be able to make sure it was being executed from a gnome-terminal and not a regular login. It's going to be complicated to accomplish, but it's possible.
I would recommend you just use simple Bash alias to open connections to remote hosts, and call those aliases as needed.
Here's discussion I found re: manipulating gnome-terminal tabs from the shell.
And remember: The simplest solution is ALWAYS the best solution.