I hope not, and also doubt it.
They would not have bothered to bring the Model Y to production in a form that they could not fit a 3rd row. Because Tesla has a limited range of models, they work very hard to make each model cover several market segments.
Model S: Large luxury/performance sedan, (before Model 3) large premium sedan, (before Model X) luxury station wagon
Model X: Large luxury/performance CUV, (before Model Y) large premium CUV, (before Model Y) midsize performance/luxury/premium CUV
Model 3: Midsize/small luxury/performance/premium sedan
Model Y: Midsize/small luxury/performance/premium CUV
Cybertruck: Full-size luxury/performance/premium standard/crew cab short/full bed pickup (6.5' bed in a 5.5' bed vehicle length)
Semi: Short/long haul tractor
You can see from how they've positioned their cars over time that the Model Y will be expected to cover a huge range of segments until they have (something like) a Cybertruck-based SUV that is less expensive to build than the Model X, and (something like) a Model 2-based CUV. Without the 3rd row, Model Y won't be able to cover the midsize market and meet Elon's stated goal of selling more than S3X combined.
It should be noted that they are willing to go a bit off script to accomplish similar goals (see the Model S jump-seats that let it serve the wagon/CUV market until the Model X was ready).