This is possible. However querying  using membership using the Object
Model requires Sharepoint Administrative privilege (user will get
challenged if they don't have access to querying membership.

If anyone is interested, this query returns the groups and users in
a group who have permission to a specified site...

SELECT DISTINCT dbo.Webs.FullUrl AS URL, dbo.WebGroups.Title AS
[Group], dbo.UserInfo.tp_Title AS [User Name]
FROM dbo.Webs RIGHT OUTER JOIN
dbo.WebGroups INNER JOIN
dbo.WebGroupMembership ON dbo.WebGroups.WebID
= dbo.WebGroupMembership.WebID AND
dbo.WebGroups.ID =
dbo.WebGroupMembership.GroupID INNER JOIN
dbo.UserInfo ON
dbo.WebGroupMembership.MemberID = dbo.UserInfo.tp_ID ON
dbo.Webs.SiteId = dbo.UserInfo.tp_SiteID AND
dbo.Webs.Id = dbo.WebGroups.WebID
WHERE (dbo.Webs.FullUrl LIKE N'%nameofsite%')
ORDER BY dbo.Webs.FullUrl, dbo.WebGroups.Title