Will a shaker work with a 440 6 Pack on Stage VI heads with the spacers? Or will the geometry be off?

It will be higher for sure, but maybe close to still fitting.

Geometry will be off the carbs will sit higher, but it could be made to work by modifying the baseplate I am sure.

Not a good plan I don't think. With a stock height intake you would be maybe an inch too high? Pretty unlikely you will be using a stock height intake so now you'll have to deal with dropping the baseplate a number of inches and still making sure you have decent flow squeezing between the air cleaner lid and the top of the carb.
Are the issues dealt with already that tag along with the Stage Vi heads themselves?

You could go with a stroked 400 block and stage VI heads, which should allow you to use a stock height dual plane RB intake.

Thanks for the responses guys. I think it might be easier to change the heads if I can't modify the baseplate.

There was a lot of information written in the Unlawful section of moparts of this subject. If the 440-6 Eddy or Wei. tunnel rams fit under the scoop of an E Body and I know they can because John Fenn from my area of the world that set many super stock records running a 1970 440-6 Cuda he bought new can fit it under then a stock intake should have no problem. The 6 Pack tunnel rams are quite high compared to stock intakes. You need to measure. Lots of times the seal ends up being compressed to the max on the adapter ring. I know this by running many a higher intake than stock on my Hemi Shaker, like a Rat R. I run a modified single four base plate at present because of the height of everything like the intake and carb, carb spacer and other things that have raised the height.There was nothing out there when I did this and modifying was the only way to do it. Measuring is the best way.

Do a google search on John Fenn SSGA Cuda and take a look at his car.

Thanks for the responses! Looks like I will have to modify the base plate

Not sure that is going to work. I had them on my old 440-6 Charger. There was zero chance the factory hood would fit.... even with the stock heads the lid was in the padding. You have to use spacers between the intake and head. It raises the intake (and everything attached to it) 3/4"

The base plate is already "dropped" If you drop it much more the carb horns will be right up on the lid.

I run a stage V intake on my hemi cuda that it slightly higher than stock and it works with my shaker.