Not effectively. Whichever chain ultimately wins still defines the outcome of "double-spent" coins, so if they tried to double-spend, one transaction would still be rejected when its chain is rejected by the mining community.
If I understand correctly, the only way to do this would be to get a private chain longer than the typical number of accepted confirmations, which is currently 6 for most merchants. In this method, you spend the coins, wait for 6 confirmations, the merchant ships the product, and then you reveal a longer chain where those coins were never spent. However, getting a chain advantage of that length is extremely unlikely without a massive fraction of the network power.
The attack described is for pools where they lack a majority of the processing power, but still have enough power to occasionally make chains at least a couple blocks longer than the rest of the miners.
If I understand correctly, the only way to do this would be to get a private chain longer than the typical number of accepted confirmations, which is currently 6 for most merchants. In this method, you spend the coins, wait for 6 confirmations, the merchant ships the product, and then you reveal a longer chain where those coins were never spent. However, getting a chain advantage of that length is extremely unlikely without a massive fraction of the network power.
The attack described is for pools where they lack a majority of the processing power, but still have enough power to occasionally make chains at least a couple blocks longer than the rest of the miners.