I believe they made a change not that long ago that adventure mode (for non-season; seasonal play is unlocked in seasons) no longer requires ompletion of the campaign.
Having said that, you also only needed to complete the campaign once to unlock it account-wide so if you’ve done that you don’t have to worry about it. Keep in mind that you cannot do GRs until level 70 so you’ll have to level your necromancer first.
Edit: I’m correct and the change was made this very patch:
H/t @Perusoe for their page linking to all the patch notes.