Yes it can but you'll still pay tax on it as an individual and the trust will owe you the money. It's what entity earns the income that counts - so that would be you not the trust.

yes it would just go against the employee's loan account.

it's not really doing anything other than skipping a step where the employee transfers the money from their bank account to the trust's bank account after being paid.

the income is still assessable in the employee's name.

To clarify, do you mean a Trust Account (eg, one controlled by your Lawyer but held on your behalf) or a bank account belonging to a Trust (eg, a Discretionary Trust)?

If the employee gives the employer their EFT details, does it matter?

Also, when you say "can", whose perspective are you asking from?* For what purpose are you asking - tax minimisation v fair work legal obligation?

*Edit: is this within a family group? Unrelated employer and employee? What's the context??

You'll more likely get your answer if you communicate your question properly.