Chasing Embers- A minor point, but since we're getting scientific: The xylem and phloem do move nutrients and moisture throughout a tree, however, this is restricted to the outermost living tissue, which is surprisingly thin, even in very large trees. I studied forestry a long time ago, but I'm quite certain of this point.
It is why you can kill any tree by girdling it, which is to remove a complete ring of bark, including the xylem and phloem. In many trees, this is about a 5-10mm deep cut. The rest of the wood that actually makes up the structure of the tree is dead.
We would need to assess how much of the dead structure (likely the entirety of your pipe) remains effective at transporting water after cellular decay.
I'm not attached to the answer. It's just like comparing apples to oranges if you toss the argument of xylem and phloem being used to transport water/nutrients. Timing may be critical.
All that aside, it seems like those who have tried it have reported that within some reason that is pretty logical, there is no ill-effect. My pipes are also a testament to this. Low cost, higher cost, it didn't matter. I know what a wet pipe tastes and feels like. It's not the case. I even tossed in my meerschaum for good measure (and that is a huge can of worms left mostly unopened) to no ill effect. If you soak your meer and let it sit for hours or many long minutes... who knows. But a quick wash did nothing.
Again, as has been said, it's not like you would wash them after every smoke. This is really overthinking it to the extreme.
Suds up! It may feel like a walk on the wild side, but it's really no big deal.