Yes, you can go to the Transak widget on their website and check your pending order there:
Note: If Transak does not automatically log you in, you will need to manually login to your account on the My Account tab.
You will have the equivalent amount of native currency for the chain your transaction was on.
For example, if your transaction initiated on Polygon, you will have MATIC in your wallet on Polygon. You can try the transaction again using the native currency (video below).
Your funds will be deposited into your wallet address in the Native Currency of that Chain.
You can submit your transaction through the widget using the Native Currency instead of the Fiat Currency (video below).