If I conquer on Sigil of the Storm Battlefield, can I use a seal to cycle the rune to complete the Battlefield requirement?

No, you cannot use a Seal to pay for the recycle cost required by the Sigil of the Storm battlefield.

According to the FAQ for Sigil of the Storm:

• "Seal of Rage cannot be used to pay for Sigil of the Storm's recycle cost. Seals can only pay for Power costs, while Sigil of the Storm specifically requires you to recycle a rune."

While recycling a rune normally generates Power, the battlefield's ability specifically mandates the action of "recycling a rune." Because this is a specific requirement rather than a general "pay Power" cost, you must actually recycle a rune card from your rune deck or board. You cannot substitute this action with a Seal or any other method of generating Power.