I think there is a misunderstanding. I am not sure that any average AAA players cost $5 million or $6 million - according to the great "AAA-just the charts" post - the salary range of average AAA - the ones that are available in any OL is from $1.75 mil to $2.6 mil for position players, from $950K to $1.85 mil for starting pitchers and a little less than that for relief pitchers.
After you have drafted 25 players, you will get a prompt to draft up to 6 position players and up to 2 pitchers, as happens in any "you pick 'em AAA" league. But first you have to put the league number in - so if you are starting with an ordinary OL draft center, click "change league option" then click on "existing theme league" and put the league number: MLB101175 in, and then click to return to the draft center. Once you have drafted 25 players, you will have the option to pick AAA players, but the only ones that will come up will be the ones within those average AAA parameters, no $6 million men I am afraid.
But the answer to the other part of your question is no, just as AAA players in no way count against the $80 million salary cap in an ordinary OL, these do not affect in any way the $70 million cap. They "don't count" as it were - HOWEVER, remember that if you make it to the World Series in this league, these players ACTUAL salaries, not 200K, will count toward the salary limit of the TOC you are placed in, IF AND ONLY IF they are still on your major league roster after the transaction deadline and the end of the season, otherwise they do not affect it in any way.
HOWEVER (2), since this is a $70 mil. salary cap league, if there is a $ 70 million salary cap TOC (which having been in only one WS ever I don't know) you are only eligible for it if you have NO AAA on your roster at the end of the season, since for TOC purposes ONLY this would count towards pushing your overall team budget over $70 million and rounding up put it into an $80 million TOC instead. So if that matters to you you want to think about that once the season is going on but it is not a factor until the transaction deadline hits.
I hope this has not confused anyone further. But I think this should be straightforward now. Good luck.