It would be fine for off road, but on the street it would be a pain.

No centre diff would mean that the front and rear axles would have to turn at the same speed. This would appear to be fine in a straight line, but once you start to turn a corner the rear wheels take a slightly tighter corner than the front, so the axles are trying to turn a different speeds. The prop shafts and halfshafts would tighten up until one tyre slipped or something broke. This is called windup, and is the reason 4x4s wear tyres if they are left locked in 4x4.

You also get problems if the tyres are inflated at different pressures, or have different tread depths.

The best setup for the street would be centre and rear LSDs with an open front diff. This stops the steering getting too heavy at low speeds i.e. when parking.

Hope this helps.

The best setup depends on what you are going to use it for.