Yes, he did, but one has to wonder how much Near understood. It never goes into great detail about how Near got his information, just tidbits about his own investigation that lead him to the same conclusions as L.
I for one doubt the term "Shingami" would have been used by the cop. Very few people touched the notebook, and those that did shouted about a monster. At that time they didn't know what to call the thing standing in front of them. The most the cop could have told Near woudl be that. He would have been unable to described what the creature looked like. Plus, if Near was any sort of detective, he should have weighted the "evidence" provided by the cop heavily. At best, it was circumstancial, and the best Near should have deducted was that something very strange happened that night.
Real prove would have come from Mello, who actually got a notebook. But again, even Mello's investigation methods for why he would conclude there even was a notebook are shady.
Man the second half really had some shitty writing.
Did you ever look at a picture of yourself and see a stranger in the background? Makes you wonder how many strangers have a picture of you.