Ohtani is not formally a part of this process... but yes, teams have limited international signing pools, so any dollars committed to ex-Braves prospects are not available to woo Ohtani. So while the Braves rulings don't formally affect the Ohtani situation, clubs will have to decide how to commit their limited dollars.
The new agreement with NPB, as reported by Jeff Passan at Yahoo (linked above by bkox), indicates that the posting period for Japanese players is November 1 - December 5... so we can expect to see Ohtani posted between now and December 5. It's probably no coincidence that the signing period for ex-Braves prospects opens on December 5!
It's not clear from the Passan article how long the bidding period for Ohtani (which commences December 5) will run - the article indicates that the MLBPA proposed a month-long period, but gives no indication as to what what agreed...but it appears that Ohtani will be "on the market" at the same time as the ex-Braves prospects. The one difference here is that Ohtani cannot be signed during that period using 2018-19 pool money - that particular flexibility applies only to the ex-Braves prospects.