The CTA is a Common TRAVEL Agreement
BUT
It does not grant any rights to permanent residence, to take employment, start a business, to receive benefits, healthcare etc
It does not cover the right to bring goods over.
It enables visits to family / friends and for tourism, cultural exchanges
but nothing longterm and nothing commercial
In practice, anyone can go from England to NI, then across the border to the RoI;
their passport wouldn't be checked
If there is a no deal Brexit, then I would expect the RoI / EU to use an emergency WTO waiver stating that due to the unique historical situation / recent Troubles
and because of the tiny % of EU imports that come through NI,
that there would be a light touch border affecting only large goods vehicles.
Maybe involving checks for larger businesses at the NI end and then transporting the goods via sealed vehicles.
Few WTO countries, if any, would challenge this light touch proposal for such a special case involving such a small population.
I also expect that there would be an RoI policy, official or unofficlal, to discourage importing British goods to any business that also exported to the RoI.
Because of the danger of British goods still getting into the supply chain, this would lead to a sharp eeduction in importing British goods