Thank you for reaching out to us.
The halachot regarding potential chatzitzot, barriers to immersion, on the hair are particularly stringent. Even without beads, women are generally instructed not to immerse with braided hair, which can interfere with water reaching every strand. Beads would add a further barrier between water and the hair.
Therefore, you should not immerse with a hair wrap. Perhaps you could devise a clip-on alternative, beads with a similar aesthetic effect that could easily be removed for immersion.
We hope this helps. Please let us know if we can be of further assistance.