Maybe, though at this stage, I don't think the EU is opposed to Parliament playing a larger role in negotiations. Indeed it may just be the 'shock' that breaks the impasse and opens up new options which May's mix of deception, inflexibility and indecision is unlikely to achieve. It may also worsen problems; but the EU won't know that until it gives it a go. And if it ends in further gridlock, it arguably only brings a second referendum a bit closer (which the EU would support).
In reality, it's hard to see how anyone would grant the concessions that the jihadists are demanding. No amount of rethinking on the backstop is therefore likely to do the trick save May and the EU tearing it up for all practical purposes. They are demands, made in bad faith, designed to call May's bluff and distract from the fact that the swivels have everything to lose in a May's WA or delayed Brexit situation. The problem for May is that her deal needs more than the support of a few swivels and other groups are quite happy if Brexit is delayed.
Of course, nobody knows whether Olly Robbins revelation earlier this week is legit - May's shown very little evidence of putting the national interest ahead of political vanity and the pointless quest for Tory party unity. With the clock ticking, I suspect MPs and ministers will be in no mood to take any more chances and will therefore push through Parliament the legislation that narrowly failed last month.