That's where I always look when trying to find someone descended from a 19th century Brit. (Like me.) People from the US tend to join there only if they have recent UK ancestors, I find, that being kind of what it's set up for.
To explain -- when you join (really cheap), you can create your own family tree at the site. Other people may only view it by invitation, but everybody can search the site and see who has matching individuals in their trees. For instance, if I'm searching for somebody who shares my Sankey line (as described in a post in the George Bush thread), I can search for Sankeys born in Kent, narrow it to born 1790 +/- 10 years or 50 years or whatever, add a first name or not, and see whether any of mine pop up. I tend to put only direct lines in my own tree, so if I want to find someone who is related to my grx2 grfather's brother, say, I have to do the search rather than waiting to be found.
Anyhow, nobody there has a Phineas Bates in his/her tree. ;)
There are two people with Wisconsin Bates-s, born 1851 and 1947. I can PM them and inquire if you like -- not mentioning the treasure trove or dates, just asking about the name, died before 1900, say.
In case they're mentioned in the info you have, they are:
Doris 1947 Prairie Du Chien, WI, United States
Elida 1851 Mineral Springs, Wisconsin, USA (could be the Eliza J Bates in Portage in 1860?)
The 1880 US census is pretty short on Bates-s in Wisconsin; none, but three born there:
Charles Bates (spouse Louisa A.) Clark, WA abt 1854 Wisconsin Self (Head)
Robert H. Bates (parents Stephen, Mary E.) Clark, WA abt 1852 Wisconsin Son
Willard C. Bates (parents Stephen, Mary E.) Clark, WA abt 1860 Wisconsin Son
Louisa and Stephen are from Canada, Mary is from Ireland, and Stephen's older son was born in Maine. Although Stephen's father was born in NY, and I think he shows as born in NY in another census; Stephen was born abt 1802.
Don't see anybody who looks like the Phineas you have, in the earlier censuses (I don't pay so can't access full info), except for maybe one in Windsor, Vermont.
That one appears here:
http://coplien.com/family.php?famid=F12646The "no recorded children" could be inaccurate.
There's someone at GR who has a Stephen Bates born 1805 "prob Vermont or New York, USA". If your info shows a Stephen, that might be worth a shot too.
The 1851 Canada census has a Stephen Bates born 1797 in the US, with a load of kids born in Ontario ...