Is it a good sign if your website looks like a plaintext file with hyperlinks when the stylesheet is disabled?
It's a positive sign, yes. What you've done is separate content from presentation, and from what you've described CSS is doing it's job exactly as intended -which is styling the content.
In the long run all you need to do is update or change the CSS in the event of a redesign. Your content will stay consistent throughout as you've kept it in the HTML.
This question seems simple but we can take it in a wider sense.
Quick answer is yes, your formatting should rely only in CSS, and without it your page should look a plain text with links.
More or less. Because HTML elements also have their indeed formatting and rules. Tables, quotations, lists, fieldsets, inputs, headings... All those elements usually renders a little different, even in a plain text context. Composing good html is the basis for a lot a things, like SEO, and can help avoiding some dummy markups, like
Of course, the simplicity to maintenance, keeping all CSS in one or two files are the real great point on using CSS.
Last comment is: don't forget images. img tag exists to be used. Sprite technique is indeed efficient, but should not replace the content images. A quick example: an image gallery.
Menu icons and other graphic elements that aren't content can and should be placed within sprites. But the images, the real content, should be placed as img tags, with all resources (alt, title, caption when inside a figure element...).
Yes, this is the best thing. It gives you the flexibility to apply another style on the page without affecting the content.