So the answer is? No.
From the Esri Support Forums: Edit spatial data with “ArcGIS for Desktop 10.1” in non-SDE RDBMS systems?
ArcGIS Server 10.1 will include a new technology component called Spatial Data Server (SDS). It is a separate installation from ArcGIS Server and will be included with all editions of ArcGIS Server. SDS is a low-memory footprint application that enables you to publish feature services of your vector data stored in a database or geodatabase. SDS will allow you to edit spatial data in a standard database and does not require ArcSDE technology. Editing for SDS is done via the REST API only which
ArcMap does not support at this time[editors note: see below]. Oh snap, not only can you not edit spatial data in other RDBMS without Esri’s Spatial Data Server, you can’t even do it via ArcGIS for Desktop. [editors note: see below] To be fair though, Esri’s business model is built on being the middle man to everything.
I don't know how this whole business started Of me thinkin' that I could edit PostGIS But if you think that we'd be better parted It's gonna hurt me but I'll break away from you
Craig Williams clarifies a key point:
Derek’s comments about ArcGIS for Desktop 10.1 not being able to edit SDS are incorrect. ArcGIS for Desktop 10.1 can edit SDS and all other types of ArcGIS feature services. These edits are performed via the REST API for SDS and hosted feature services.
So what does that mean? Says Craig
you connect to SDS, drag the service into the map and it draws via REST calls. To edit you check out / check in
So the final word on this is that you still need middleware to get this done, but you don’t need ArcSDE anymore. Esri views editing spatial databases differently that many of us do, I don’t fault their thinking too much on this, but 99.9% of the time in the real world no one cares about deltas. So to fix my thoughts from above:
Oh snap, you can’t edit spatial data in other RDBMSs without Esri’s Spatial Data Server.