I don't think so. Labour are for 'a'/'the' customs union right now and their manifesto rules out a 'no-deal' Brexit. Corbyn (or the left of Labour) have no issue with EU regulations regarding employment rights, the environment or other social protections. That makes aligning with the EU much easier than it does for the Rees-Mogg/Gove wing of the Tory party. In other words, the most Eurosceptic Labour MPs are already quite happy to do a deal that aligns with many existing EU regulations. Then a huge chunk of the Parliamentary party, members and trade unions want to stay in the single-market.
The Rees-Mogg cranks want a hard Brexit so that we become a low-regulation economy with little in the way of worker's rights. Corbyn isn't cut from that cloth, quite the opposite.