In reference to virtual cards:
No. Your full credit card details are only stored in a secure tokenized* form. Your credit card number, expiry and CVC number are not stored in MySudo, only the card type and last 4 digits of the card number are stored.
Therefore in the event someone gets access to your phone and MySudo, they will not be able to access your important credit card details.
*Tokenization is the process of replacing sensitive data with unique identification symbols that retain all the essential information about the data without compromising its security.