Hi
It is possible to create destination cookie/Storage for each segments and It will be delivered to the website
You will come across lots of issue when you have lots of segments
I believe you are taking wrong approach. this technique is use to share segments for Non-Adobe platforms.
Target and Audience should be part of the same Org and this will allow selecting segments from Target. Audience segments will be prepopulated in Target and those segment will be qualified in runtime
Talk to Adobe client care to connect AAM to your Target
Thanks
Abu