Hi,
No ; that is not possible with the Paypal plugin.
When you send the customer to the paypal website ; you need to gave him some information, like an order id for the reference.
So when Paypal confirm the payment, you have an order to confirm.
(And for sure you can't use the cart because the customer will be able to modify it so it's not a "safe" element).
But using HikaShop Business, you can use the "automatic cancel order" plugin which will cancel every created orders after a certain period of time.
That plugin uses the cron trigger system ; that's why the plugin is provided by commercial edition of HikaShop.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.