bill - 1:22 am on May 28, 2010 (gmt 0)

does an RSS feed from Feedburner get spidered on the subsequent websites where it is being displayed?

That would depend on how the feed is integrated into the site. If they're presented in a spiderable format they will be looked at the same as everything else on the page.

Do the outgoing 'links' on those sites (within the RSS feed) therefore count as backlinks to wherever they be going to?

If the links are on the page, and the site owner has not nofollow'ed them or run them through a redirect of some sort, then why would they be treated any differently from other links?