Hope this is not repetitive from above, I scanned the thread:
Google has stated and it has been implied that 'serious' sites are more likely to have certain technical things in common. Among them, a dedicated server (or servers), unique IPs, long-term domain registration, etc.
Of course this goes into a huge mix of things they look at, but it is pretty much beyond dispute that if you get "checkmarks" in these areas as well as unique content, non-affiliate content/links, solid and related inbound links, etc. etc. you have a better chance at being ranked well .... so, short answer:
Yes, but also try to be seen as a "serious" site in as many other criteria as possible - just having a unique IP won't likely do much.
