Yes, if you don't update WP or the theme itself, it should remain the same. AND congrats for being aware of this - many newbies do not know this, and are alarmed that a WP upgrade has changed their site, because Twenty Ten is standard WP equipment.
Your manual method could work just fine, assuming you only made changes to style.css! The only caveat to that would be if the powers-that-be have changed the the theme in the meantime, along with making changes in style.css. Then when you paste your stuff in, some new stuff could get lost. So if you're very fastidious, you could do a code compare of your saved version with the new version of style.css. A quick look in the WP themes directory shows that the last update of Twenty Ten was in July of 2010, and it's at version 1.1 now. That's around the time of the WP 3.01 release.
But your method is, in principle, excellent. I have had to use the same method with the Construction theme - it has its own special sections for your own CSS tweaks, which are handy, but these are overwritten when updating the theme, a slight but manageable annoyance.
I am, however, a big proponent of child themes... this is such a great concept, and when you get more comfortable using WP, you might reconsider using them.