Benjamonkey, the flat bottom on the engine compartment will have some major and some minor effects. Major: reduced drag, generally more downforce on the engine bay end, hotter engine bay. Minor: difficulty working on the engine, possible component overheat (starters are most likely), vibration from the flat panel. You didn't mention what type of car you are planning the project for so the balance change you are asking about is dependant on the car layout. Front engine cars will add some front downforce to an already front heavy (aero-wise) platform. Rear engine cars will gain rear downforce where it is needed most.
The drag aspect is going to be the most sensitive change for a street car with relatively high clearances. If the panel is fitted without regard for the incoming air direction, you could wind up adding drag. The drag change will be seen most effectively in mileage or terminal top speed (not suggested on public rodas!!).
The downforce and balance aspect will only become noticable if the car is quite close to the ground (less than 2"). You may be able to determine the downforce change by checking the change in shock travels before and after (knowing the spring rates at the wheels and using a smooth test area).
Cooling may be your biggest issue. If the engine bay is completely sealed, then no air will get in or out. If there is an inlet and no outlet, the engine bay get pressurized (very slightly) and then no more air gets in. You mentioned exits in the hood, which will work at speed, but may need to be enlarged. Also keep in mind that the airflow directed to the hood exits will probably allow other items near the bottom to get hotter than normal. I would suggest adding some small exit vent in the flat panel at the bottom of the engine bay to draw heat away from some of the components.
Roughly the same amount of energy that goes to the wheels is cast off from the engine as heat, so there is quite a bit of energy to deal with.
For your project you may want to define it a bit more as far as drag reduction or downforce increase/balance change.
Steve Stafford.