Firstly - while shift speeds are quicker than a T56 manual - this is offset by the loss of power to the rear tires on lower power cars (eg. 500rwhp). This loss of power is expressed as heat.
The cooling required to keep an auto working throughout a real road race will require considerable thought and space.
Auto's have been successfully raced at club levels, but will never compete with a good driver on a quick shift manual box due to the power drop and lack of engine braking. A sequential box like a Holinger will shift just as quick as an auto with far less weight, heat and power drop - so will be quicker - and by quite a lot.
Drag racing is different - and when you start ramping power up like with turbos - then an auto becomes a great option because power shifting a manual with 1500rwhp is never going to hook whereas the progressive and smoothness of a well sorted auto will be better at getting power down and the extra power it soaks up is more than offset by this. The heat is more easily managed too than in road racing where power is applied over a long time generating heat soak.
Secondly: it will not fit without extensive body work. Adding a Gear Vendors will make for a very short driveshaft. For the time and money spent cutting up the car and making the 4 sp Ram box work you might as well just go buy a Holinger which will be vastly better for road racing.
The Holinger can be ordered sequential and has no peer/equal in the road racing world for the Viper. They will shift as fast as you can move, and can even be shifted without the clutch, though you might want to lift between shifts rather than power shift clutchless. Their ratio options will ensure you can use more than the first 3 gears too.
In summary - unless you want to road race with 4 digit power - an auto offers only one advantage i.e. its easier to drive.
The downsides are:
1 - heat (road racing big power would make heat soak almost impossible to prevent in an auto) so the risk of DNF is high to extreme (esp. if you have more than 1 race);
2 - fit;
3 - loss of lap time vs a sequential or even a T56 due to power loss, slip, weight, lack of engine braking;
even if you can keep it alive for a race, you will be rebuilding an auto after every race weekend - guaranteed. Auto's HATE excess heat. You may make it work for 4-5 hot laps on a club day but that is a LOT of trouble to go to for something that could not handle a real race IMHO.
Not saying it cannot be done, just saying the obstacles are going to cost you way more than you imagine to overcome.