Thank you for downloading Boldly Go Blue, and for posting your question in the forums.
Secondly, rather than try to add the Google Analytics code manually, I would highly recommend using a plugin to do this for you. You could use the one that CrouchingBruin mentioned. There are many others. I like Yoast personally, he does great work, and he has created a plugin called Google Analytics for WordPress. You can install it with just a few clicks from your installation's Plugin Administration menu, or click here to download it from the repository.
Finally, I don't think you have to worry about dire consequences :) As with all WordPress themes, you're welcome to change the source code yourself, and there is a convenient code editor within your wp-admin that will allow you to do this without any special software. In this case, "Boldly Go Blue" is already a child theme of Stargazer, so it inherits the parent theme's functionality. The author of the parent theme discourages people from modifying it for the reasons you stated. The child theme, on the other hand, simply makes some changes to the colors, and gives the navigation menu a fixed position. You can't do much to mess it up; and if you do, you can always re-install it and start over.
If you have any other questions, let us know.