No, this is because what OpenSea does is collect a signature from your wallet and hosts it on the site.
When a user goes to look at your asset, OpenSea shows them that signature and if they so wish, they can bundle that signature, along with a transaction that they broadcast and pay the gas fees for. The OpenSea marketplace contract will then execute the trade, using your signature as proof that you did wish to sell the asset for the given price within the given timeframe.
This is also true for things such as bid offers, OpenSea hosts them and the owner of the asset can use that signature to execute a transaction in which they sell the asset to the bidder.
This is also why when you are cancelling bids / listings on OpenSea, a gas fee (sending a transaction) is required. A malicious actor could save the signature for later use (OpenSea freely gives the signatures out), and then use it in a transaction to purchase your asset (vice-versa for bids). Cancelling a bid / listing will send a transaction containing the signature you previously generated, with instructions to disallow that signature for further use. This of course incurs a gas fee.