No. Refunding or cancelling an order never restores the coupon:

• Available Quantity is reduced by one the moment the order is placed, and nothing in a refund adds it back — a fully refunded order still counts against the coupon's remaining quantity.
• Limited One Use per Customer works the same way: Sprwt checks whether the customer has any past order that used the coupon, with no check of that order's status. A refunded or cancelled order still blocks the customer from using the coupon again.

If you need to let a specific customer reuse a one-per-customer coupon after a refund, or need the quantity back, you have to edit the coupon manually (raise Available Quantity) — there is no automatic reset tied to refunds.