That’s not necessarily true, there are other reasons such as e-mail may be temporarily deactivated, or they have banned your sender (which also may be temporary, as in a temporary account silence).
First step I would recommend for what you are describing would be to send a regular PM to a user if their e-mail isn’t receiving messages as an alert about that in case they aren’t aware, you can make that an official warning PM with the checkbox to make the envelope alert icon red instead of green. This also puts a note on their account that they have been sent one or multiple official warning PMs so you’ll have that documented.
As mentioned with the default settings new accounts must be validated by clicking link in verification e-mail firstly before they can use your site, unless you have bypassed that.
That seems to be basically already enabled with the default settings, although TL0 can post public replies/topics they can’t send anyone PM messages until they are promoted to basic level TL1, which requires some reading and e-mail would need to be validated before that.