No not really. Yes, you can set a reference to Microsoft Internet Explorer and a reference to Microsoft HTML Object Library. This will allow you to access the DOM object model directly, and the intellisense will work. But if you actually try to access the property, it will throw an error. (As demonstrated below:)
Option Explicit
Sub Example()
ThisFails "http://www.w3schools.com/html/tryit.asp?filename=tryhtml5_webstorage_local", "lastname"
End Sub
Function ThisFails(ByVal sURL As String, ByVal sLocalStorageVarName As String) As String
Dim oBrowser As SHDocVw.InternetExplorer
Dim hDoc As MSHTML.HTMLDocument
Dim hWin As MSHTML.HTMLWindow2
Set oBrowser = New SHDocVw.InternetExplorer
oBrowser.Silent = True
oBrowser.Navigate sURL
oBrowser.Visible = True
Do
' Wait till the Browser is loaded
Loop Until oBrowser.ReadyState = READYSTATE_COMPLETE
Do
Set hDoc = oBrowser.Document
'Trust me on these loops
Loop While hDoc Is Nothing
Do
Set hWin = hDoc.parentWindow
Loop While hWin Is Nothing
ThisFails = hWin.localStorage.getItem(sLocalStorageVarName)
End Function