An impedance of over 2.5k does not make the ADC fail to read, it is just off a few codes. Longer acquisition times help some.
The point being that the 2.5k forms a voltage divider with the output resistance of the sender. That output resistance must be significant to motivate such a strategy, it's often inconsistent and somewhat ill-specified as well.
It also decreases the amplitude of the signal, which decreases the accuracy of the ADC. Using an external, lower vref might be needed to try to compensate.
Overall this will decrease your accuracy far more than using a source greater than 2.5k ohms. I've never heard of it being an effective strategy.
If you have a moderately high output resistance, like 5k, and don't need high accuracy, I'd investigate whether this will yield acceptable results. If not, buffer.
But you mention a pressure sensor. These are almost always a strain gauge bridge which means a differential output. Since you don't describe having a differential signal, I suspect the part is one which has an internal output buffer in which case you will not see a output impedance issue.