Note that eventually, the fastest way to get into the water is via coastal cities (because they going a cheap embark), and the pathing won't know that the UI is going to give the unit a cheap embark.
As maybe the only one testing this, I'll share my experiences thus far. All anecdotal, I am not recording stats, so where I throw out % consider there is some estimation error. I have played with my "default" move in mind first, compared to the resulting moai-encouraged move.
Obviously, in early game, most of ancient, there is no difference, everything plays same, there might as well be no promo.
In late ancient and throughout classical, you are building moai -- the experience here can vary wildly depending on city layout and initial moai placement -- as human, you are inclined to pick the first moai spots as common pathing spots, and in this sense a well-placed moai might see as much as 60% of domestic auto path unit traffic over it, or none if not well placed. As human, you will manually path the majority of units to a badly placed moai, if that's all that's available, as they come out of the city the first time. It's debatable how worthwhile it is to return to moai when already far away, generally I am not bothering with deliberate reloading except on defence, when the island and moai tiles are also the combat tiles, or very closeby.
By medieval most moai are setup. Now the experience varies on city and road placement. In the case of a 1-tile inland Island city, the Polynesia specialty with current UA, the moai promo toggles via auto-path like 80-90% of the time regardless of roads, maybe even more if you're just doing moai and no other improvements on coastal plots. Sometimes though, you need to build a non moai, or would otherwise like to, and sometimes these land in key pathing spots, which can honestly drop the auto pickup to somewhere near 50% in rare cases where one tile is just much more useful for embark/disembark. As human you just road into next best moai tile and this usually boosts auto pickup back up again. In coastal Island cities, units often end up pathing through the city, so maybe moai promo is only acquired around 50-70% of time without deliberately trying to. Road placement helps once again.
On coastal mainland cities, obviously presence of promo via non-deliberate acquisition drops quite low. Roads do help when expanding along the coast rather than inland, but the promo becomes pretty much non existent the moment you begin pushing perpendicular to coast line.
There are special cases where I have to send units to a far off island very quickly, and will often divert units already deployed to some other task -- if the far off destination is far enough, I will deliberately even reverse course for 1-3 turns to pickup promo. 0% automatic pickup in such cases.
Another unique use they requires deliberate planning. Coastal roads into moai can be very useful for archer defense of water tiles, and I very deliberately look for opportunities to set these up. Consider that archer adjacent to water vs naval benefits from stronger attack and ability to move away -- with good moai roads this is almost always on and 2-3 archers can be quite lethal island defenders
Once cities become the preferred embarkation point, roads will decide whether any further auto pickup occurs. Acquiring the promo does become much more deliberate in most cases EXCEPT 1-tile inland Island cities, the preferred poly configuration. Well placed forts also help.
So human has access to some improvement and road placement, as well as detour knowledge that probably boost its ability to acquire the promo somewhere around twice as often as the AI otherwise will meander blindly into it. The gap closes somewhat in island defense applications for which this was intended to be most impactful.
While this is nonetheless a substantial gap in usage, I remain a proponent on the basis that the promo effect itself, as only ever a 1-combat advantage, is subtle, and the effect of getting the promo more often in broader gameplay, as human will over AI, is also subtle. Despite being subtle, it is also a FUN feature to plan around, opening up some coastal ambush and surprise attack plays that did not exist previously. The moai promo is most effective for both human and AI 1-tile inland cities, and thus well on target for poly current UA.
TLDR AI will probably make use of this mechanism to around 50% of optimal effectiveness. It is most effective for 1-tile inland Island cities, where human and AI will be closer in their usage, and all but useless for fightng inland. Later in game requires more deliberate planning, widening gap between human AI usage. Promo effect is fun to play with but subtle enough to blur some of the human AI disparities