Rental bike for holiday: wise to change handlebar style?

I'd recommend getting used to a new handlebar style (or frame geometry or any other change) slowly. On a multi-day trip problems tend to accumulate, so I would't recommend trying anything new. An additional problem with drop bars is that the brake and shift levers work differently and some people seem to have problems getting used to them.

You could try to rent a bike with drop bars at home and see how it works out.

Edit: For the kind of trip you are planning, many cyclists prefer drop bars. I would recommend trying out them if possible.

You haven't mentioned what a "cycling vacation" is for you: Is it a four-day wine tour in France, or is it a month-long trek across Kazakhstan? You mention "100+ km/day", which implies a decent pace, but it still leaves the riding style open as to how often you take breaks, how tough the terrain is, etc.

Easy/short/safe rides

The closer you are to civilization and the more frequently you take breaks, the less important the actual handlebar choice is: If it's not comfortable or you don't feel confident using them, take it slow, take more breaks, etc. If you really don't like them, spend an extra day relaxing in some nice town and cut your trip a bit short. The cost of changing out handlebars in terms of money, time and hassle just may not be worth it.

Hardcore tours

On the other hand, if you're going to be in the middle of nowhere and absolutely have to e.g. get across those mountains and to a specific village by nightfall or else you're in big trouble, the costs of using a new handlebar style may be more critical. In fact, if this is the type of tour you're envisaging, the "cost" of renting and riding a bike you're not used to (and possibly don't trust) may be higher than the cost of bringing your own bike along.

Most countries drive on the right (including probably yours, but not mine). In Japan they drive on the left. Driving etiquette is also very different in Japan (we've had questions here about some aspects that affect cycling and are non-obvious).

Unfamiliar bars (brake location, lower head position affecting your view) and unfamiliar traffic habits aren't a good combination.

I've also found the fit on flat bars to be more forgiving (get the saddle height right and I can jump on and ride for a few hours). Even though my tourer is a very good fit it still took some getting used to at first and I'm not sure a multi-day trip is the time to do that. Your back could well suffer. Drop bars may be more aerodynamic, but not by enough to make up for a bad geometry you can't adjust in the field, and if you're touring with a slow group, being able to blast round and get off the bike sooner isn't much help.

I'd stick with what you're used to.