No, she is not. There is just too much evidence against it.
In TLJ, Snoke was playing her the whole time, spanked the side of her head with her own weapon, ripped Resistance secrets from her mind and left her at Kylo’s mercy. Kylo then had to save her because she was having trouble with one member of Snoke’s Honour Guard (the rest were chopped down by Kylo himself).
TLJ was punctuated with her failings. She almost fell to the Dark Side during her first formal lesson in Force Training, needed a lightsaber to beat an old man armed with a stick even though he had closed himself off from the Force, and she was such a disappointment to Luke that Yoda had to talk him into re-joining the fight. Her efforts to pull Kylo back to the Light resulted in him choosing the Dark, and despite having a head start on him, was the last person to show up at Helm’s Deep, too late to even participate in the battle, let alone turn the tide. None of this would have played out as it did had she been a Mary Sue.
All she accomplished was the opening of two doors: moved some rocks to get a handful of soldiers out of a cave, and then let them onto a spaceship. Of all the heroes in the movie, she was the least accomplished. She had nothing to do with the bombing of a Dreadnought (a class of ship the Resistance had never managed to destroy before), the infiltration or destruction of Snoke’s warship, or even the Resistance’s Hail-Mary sprint to Helm’s Deep.
Hell, the movie even said that she wasn’t anyone special. Had the Force not chosen her to be a balancing agent for Kylo, she’d still be trading scrap for food and fending people off with a stick. Even as a pilot she isn’t noteworthy.
While Han Shot down Darth Vadar’s Custom TIE, (despite being a petty criminal against an ace pilot combat veteran), evaded a squadron of enemy starfighters in an asteroid field dogfight and aced the timing for a hyperspace jump through an impenetrable forcefield...
Rey barely got the Falcon off the ground, required help from a trained soldier who was specifically familiar with the enemy’s equipment and tactics to barely evade/defeat them in familiar territory. Even Luke did better in his first combat flight, blowing up the Death Star as the last Rebel fighter standing whereas almost every Rebel combat veteran was shot out of the sky like it was a matter of routine. (And they were all killed before Obi-Wan had to remind Luke to use the Force).
If you’re going to lower the bar so much for her to fit your idea of a Mary Sue, the number of others clearing that hurdle would be so numerous that the entire concept would lose its special status among things worth complaining about.
She fits into the Chosen One archetype a lot better than the Mary Sue concept.
EDITS made to correct errors.