If you’re using the free version you can try using a little hack: check what happen if you copy the code of the newsletter you want to send in the “Text” of the welcome message (make sure too add the style tags in the head of the message and to not duplicate any tag).
I never tried it so no idea if it works or not … let me know.
If you want to send a special message to all your new subscriber, you can use the welcome email or install the autoresponder addon to create even more complex automated tasks.