No is the short answer!
We are currently working on a feature that will enable someone else 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.
As soon as this feature is available we will let you know.