Yes, it is possible, though not highly probable, as 25% of new students had less than a 1390 SAT score, meaning that some (though probably few) probably had a 1310 or lower. It certainly would not hurt to take the test again, as you are planning to do.
If your score doesn’t get any higher than it currently is after taking the SAT again (also you could try the ACT if you haven’t yet), I’d say to still apply if you / your family has the financial resources for it and you remain enthusiastic about NU. As I said earlier, some people with 1310s may still get in, and your high school academic performance, ECs, recommendations, essays, and the like may be enough to make up for your test scores. Who knows.
Since NU is your “absolute dream school”, you might want to consider applying ED if you do plan on applying; applicants have a much higher chance getting in there than in RD.