Probably not. If that default remote image appears on a PC/Mac you can right-click on the image and a list of 'extra' buttons will appear, probably including the DVR button. Unfortunately, when the iPad app changed to show realistic remotes Sling omitted this feature. Since the first version, they have added ways of accessing some of the buttons through extra drop down menus (all of which are actually available on the image), but have not added access to the Custom buttons which are not available on the image (logic of that totally escapes me).
All I can suggest is you install the iPhone app and run it in x2 mode. That still uses a dedicated set of remote controls which will include the Custom button and probably the DVR button.
The "realistic" remote is what I wanted and needed, but instead got a generic remote with hardly any buttons...
However, I am happy to say that NOW it is showing a realistic remote, and I am able to access all of the functions of my DVR like I wanted.
Either an update, or someone heard my cries - as I sure didnt do anything