A number of MPs seem to think so. Their argument goes as follows. Although the Withdrawal Agreement (WA) is not about trade (beyond the backstop), and trade is dealt with in the Political Declaration that is not legally binding, a vote for Theresa May’s deal will be taken by her as endorsing her wish for a hard Brexit. In that case parliament should instruct the government to pursue a much softer Brexit now, because it is better to do that now than later (especially if later never happens).
Indeed it is plausible to argue that the current impasse in parliament would not have happened if May had gone for a soft Brexit (something close to BINO: staying in the Customs Union (CU) and Single Market (SM)) from the start. That, it could be argued, was the appropriate thing to do when the vote was so close. Another way of putting the same point is that there may not have been a majority for Leave at all if it had been clear that this involved leaving the CU or SM.
The narrow vote for the Welsh Assembly in 1997 is an interesting example in this context. It was even more narrow (it was won by 50.3%). As a result, according to this thread from Richard Wyn Jones, the winners went out of their way to involve some of the losers in the discussions about how the Welsh Assembly would work.  So if May had thought about uniting the country after the 2016 referendum she would have proposed some form of soft Brexit. Instead she tried to unify her party rather than her country, and the rest is history.
Although trying to unite the country would have been the right thing for any good Prime Minister to do (as May will probably find out today), I think the implication that subsequently a soft Brexit would have passed a vote in parliament is less clear. We return again to the critical point that a soft Brexit is not a compromise between a hard Brexit and Remain. Something like BINO is, for Leave voters, worse than Remain, because it gives away sovereignty compared to Remain with nothing gained in return.
Soft Brexit is Brexit in name only, and assuming Article 50 would still have been triggered there would have been two years during which Brexiters would have kept telling us that a soft Brexit is pay and obey with no say. And for once they would have been largely right. For a country as large as the UK, having an external body choose your regulations and trade deals when you have no say in that external body is a big deal. It is the opposite of taking back control. I do not think soft Brexit could have survived public scrutiny over two years.
This has important implications for attempts in parliament to modify the Political Declaration to commit to a soft Brexit before passing the WA. I can see the attraction for many MPs: it would be the same attraction it would have had to a statesmanlike PM after the 2016 vote. But there is a distinct danger that the public will end up hating it. Remainers obviously, but also most Leavers who will feel that they have been cheated by parliament.
If you are one of the MP’s going for this option and think I am wrong, there is an obvious way forward that could get us out of our current impasse. (I first heard this idea from @SimeOnStylites.) Combine your forces with those going for a second referendum in the following way. Propose a referendum between some form of soft Brexit (softer than May’s deal) and Remain. That proposal could command a majority in the house, and would still give people the option of throwing out the idea if they preferred staying in the EU.