Just to be the odd man out....you could do it. The sand bed would be a fine filter.
An undergravel filter run in reverse flow (trading the sand for heavier grade material like gravel) would be very helpful, but – like the live rock – not strictly necessary.
You will still need significant flow, but not nearly as much without the live rock causing so much turbulence.
You have to take all this into account when stocking the tank, however.
Most fishes you read about are reef fishes and they will expect at least some degree of reef habitat. Fish that are comfortable in the open will be needed.
You will also have to pay close attention to the accumulation of nutrients while stocking the tank as you will have a smaller nitrogen export capabilty without the live rock.
This means you have to be 100% more selective about your fish picks.
Sounds like a cool challenge with some very interesting possibilities, but maybe not what you had in mind.
