No. Keywords in alt attributes may count toward word count, but no longer count towards ranking with the major search engines unless the image is hyperlinked. In that case the alt attribute takes the place of the missing hyperlink text. You are also limited to about 50 or 60 characters in total for alt attributes on a page. The rest are ignored. That prevents people from stuffing alt attributes with keywords.
BTW, although the term is commonly misused, 'alt' is an attribute of the tag 'img'. There is no such thing as an alt tag.
The best thing you can do is improve rankings is to improve the content and make sure that the keyword theme for the page is properly included in the HTML title tag, heading tags and internal and inbound hyperlinks to the page.
I agree that spacers are a real pain. I just reviewed a site that had 88 spacers on a simple home page with almost no content. A large percentage of the code was for spacer gifs. The original designer must have liked spacers.