Thinking of switching from Dreamhost to Go Daddy, would this affect my website, in terms of ranking and any SEO that I have done ?
maybe temporarily... i recently changed hosts for one of my best sites (to go to a much better host), i didn't see any significant impact. (few months ago) just my opinion.
It could be smooth, it could be disastrous. All depends on your preparation, the order you do things in etc. Start off by checking php versions etc. if that applies to your site. Bets to try a beta test privately on the new version.
what actually happens is, with better hosts, the 404 errors don't come. and the page loading is faster. these are the points why a change of host sometime affect the rankings.
Actually, it will if there is sufficient downtime, the new version has persistent errors or other websites on the same IP address are full of crap.
It may affect only local rankings. Downtime is not a problem, google will crawl again site and will see that all is ok. And you may check who else is on your IP. http://www.seologs.com/ip-domains.html