As long as she doesn't do anything against the laws of the ancients here in our galaxy, and she ascended "naturally" she's well with in her rights to leave this galaxy and return home.
Also the Ori were sharing power gained from worshipers, now Adria can claim all that energy for herself.
Of course if she truely believed in origin, and knowing the ori were dead, this should leave her with 2 good options.
Option 1, follow the book of origin and help people worship and ascend
Option 2, be a jerk and try to horde all the followers to herself, but from a militaristic point of view option 2 is a very bad idea. Just in case the ancients get any bright ideas they still significantly out number her.
Option 1 would be in her best interest so she can have back up, and she could set up an order of command of ascended beings that would be loyal to her, as well has have the worship mostly channeled to her so she could remain the single strongest ascended being.
All in all if i were her, i'd go with option 1.
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