The biggest problem that I have seen with home processors of venison is that they vastly over trim their meat and then add "fat" to put the moisture back in! Being in the meat industry and processing deer since 1969 I can can assure you that venison does not have to be trimmed to solid red only! The silver skin and internal fat (like that on the ribs) can be included with no ill effect, if the deer was properly handled.
Can you make brats with your burger? Sure. However brats are traditionally made with pork only, so making venison brats with no pork at all will result in a difference in taste, moisture, and texture.
Most processors use a 50/50 mix of venison and pork we use a 60/40 mix of venison and pork. Pork helps to bind the meat and also imparts moisture and flavor.
Dave