No is the short answer!
We are able to add someone else to your account to create a draft transaction on your behalf.
They won't be able to sign it because TrustVault is built in such a way to ensure that only the account holder has the permission to sign transactions.
The draft transaction will be created on our website and then appear in the TrustVault app. It will only be sent (submitted to the blockchain) if the account holder logs in reviews it and signs it.