Yes, it is bad for SEO when the index page has a 302 redirect.
Matt Cutts discusses this scenario in an old blog post from 2006:
for on-domain 302 redirects (that is,
a redirect in which both the source
page and the destination page are both
on the same domain), search engines
will usually pick the shorter url.
It's better for SEO when the search engines don't have to make those choices.
Incredibly, his off-domain redirect example for sfgiants.com still has the same sub-optimal behaviour today.