Please review the documentation on Esri database support policies. In short, they say that Esri
can only support versions which have been certified; later service packs are "assumed to work"
(sort-of supported if they do work, and unsupported if they don't). Most of the Esri software
baseline has shifted to 64-bit at 10.1, so the majority of the testing (and therefore certification)
has been done with 64-bit.
"Direct Connect" does not mean "Query Layer" -- these are very different technologies. "Backward
compatible" on that page refers to support for ArcGIS 9.3.x servers from 10.0 clients, not across
database releases (which I know do not work, because a minor release changed the default bitsize
of date types somewhen between 8.3 and 8.3.8).
If you connected to a 32-bit 9.05 PostgreSQL with PostGIS 1.5.1 from a 32-bit or 64-bit ArcGIS
client, then yes, it is supported. Higher releases fall in "assumed to work"; lower releases are
"unsupported" (but may work [for now]).
In general, it's best to make a snapshot of PostgreSQL and PostGIS binaries 3-6 months before
a new version of ArcGIS is scheduled to be released, so that you can be sure to find compatible
binaries when ArcGIS finishes certification and is ready to ship.
- V