Hi @erichter. Yes. It is possible. Under the PartDocument (Link1, Link2) object is a property called DisplaySettings (Link3, Link4), which returns a DisplaySettings object (Link5, Link6). That object should have most of what you are looking for. Below is a small starter sample to get you started.
If ThisDoc.Document.DocumentType <> DocumentTypeEnum.kPartDocumentObject Then
MsgBox("A Part Document must be active for this rule to work. Exiting.", vbCritical, "")
Exit Sub
End If
Dim oPDoc As PartDocument = ThisDoc.Document
Dim oDispSettings As DisplaySettings = oPDoc.DisplaySettings
'oDispSettings.AreTexturesOn = True
PS. A few of the other areas shown within the Document Settings dialog can be accessed through these properties of the PartDocument object:
oPDoc.ModelingSettings
oPDoc.Sketch3DSettings
oPDoc.SketchSettings
oPDoc.ComponentDefinition.BOMQuantity
oPDoc.ComponentDefinition.BOMStructure
Wesley Crihfield

(Not an Autodesk Employee)