Unfortunately even if you use
{ IF { REF check1 } = whatever "true" "false" }
you cannot test the value of the checkbox field because it always returns
the same null result however it is checked.

You could achieve what you want using a VBA Exit macro (i.e. specify an Exit
macro in the properties of the check box field) to insert the result
directly, or
using it to set up (say) a custom property or Word variable that you then
display.

e.g.

Sub processusepgh001a()

With ActiveDocument
 On Error Resume Next
 .CustomDocumentProperties("usepgh001").Delete
 Err.Clear
 On Error GoTo 0

 .CustomDocumentProperties.Add _
   Name:="usepgh001", _
   LinkToContent:=False, _
   Value:=ActiveDocument.FormFields("usepgh001").Result, _
   Type:=msoPropertyTypeString
End With
End Sub

then use

{ IF { DOCPROPERTY "usepgh001" } = 1 "{ REF pgh001 }" "" }

Beware of the following approach, which looks simpler:

Sub processusepgh001a()

With ActiveDocument
 On Error Resume Next
 .CustomDocumentProperties("usepgh001").Delete
 Err.Clear
 On Error GoTo 0

 .CustomDocumentProperties.Add _
   Name:="usepgh001", _
   LinkToContent:=False, _
   Value:=ActiveDocument.FormFields("pgh001").Result, _
   Type:=msoPropertyTypeString
End With
End Sub

and just use { DOCPROPERTY usepgh001 }

because it relies on the result of pgh001 being finalised at the time
usepgh001 is set, which may not be the case.

--
Peter Jamieson
MS Word MVP