On a physical or mental level, yes.
On a cellular level, nahhh

The Specialized Purist bottles are excellent. Pure water taste, three years later. Even let it sit in the fridge full all winter and in the spring that water tastes just as clean as if I would've put it in there the day before.

I’d take the Purist lotus leaf reference to mean that the lining of the bottle is extremely hydrophobic, like the waxy coating on lotus leaves, which helps prevent dust and grime from sticking to the leaves, keeping them clean and, in a sense, pure.

I’ve not read the Purist site, but I’d speculate, based on what the OP said, that a type of silicon oxide (SiO2) ceramic coating is bonded to the inside surface of the bottle. One of the properties of these coatings comprised of densely packed, tiny (nano) particles is chemical resistance, so in being bonded on the bottle surface, they inhibit the transfer or leaching of compounds from the plastic to the water.

I have certainly been around long enough to smell water bottles that had plasticky, synthetic chemical odors, and to taste the same in water from other bottles. We know for a fact that plastic formulations can, have, and do leach chemical compounds, some with high estrogenic activity levels like BPA, but many which have not been researched for impacts on humans.

Given what we don’t know about synthetic chemical compounds in the body, and given what we do know about the relationship of estrogens to cancer, it is certainly sensible to take precautions to reduce ingestng those things when possible. To that end, the small cost premium for a couple Purist bottles is the only downside to reducing the risk factor in cycling water bottles.

Couple that switch with a shift to bottled water in glass, and I think one could take some comfort in reducing consumption of water which has steeped in plastic.

Irony being, all the water pipes in modern houses these days Downunder are allowed to be PVC plastic.