stealth_nsk
Deity
No, you can't because unless duplicate civs are enabled, that would make base game unplayable.You absolutely can make the 4th age available for free and then only put 3-5 civs in it without paying for DLC. That wouldn‘t be nice in an age in the middle that you have to play, but it works fine for a tacked-on age after the third, because playing it remains optional. Then you launch it with a $50 pack that has the remaining civs and leaders …
I honestly don't understand there those ideas of "cut" content come from, but Atomic Age will come in expansion together with full pack of its civs (10 minimum, 13 pessimistic, 15 optimistic), unless Firaxis decide to change plans and scrap it. This will still make the base game playable without any problems, because the ability to finish in any age will come in one of the near future patches anyway.