Yes, I would expect that he does, but the situation is a bit different in Buddhism from other religions. There is no value attached to believing something just because you've been told it, there is no creed.
The various teachings are rather more like hints. They say - take a look in this direction and you may find something interesting if you do.
If you are totally sure that when you die, that's the end of everything, it might be hard to be a Buddhist. But if you have an open mind, and don't know what happens when you die, then that is best of all. Because keeping an open mind is exactly what the Buddhist teachings are all about.
Also in the Buddhist teachings, then the effects of karma are something we can do something about. You are not tied to them, indeed the whole idea of the Buddhist teachings is that we can escape from the wheel of suffering.
There is the idea that effects of our actions in previous lives influence our present lives - also within our life though, and sometimes is easy to see for instance strong anger can lead you to immediate delusive action which you regret when you calm down.
It's not the kind of simple minded thing where e.g. if a mosquito bites you on the nose, then you must have bit it on the nose in a previous life. Also there is no idea of a "soul" or some such entity going from one life to another; Indeed it is a good question to ask yourself, if you believe in reincarnation, who or what exactly reincarnates? It is hard to say in what way I'm the same person now that I was say 20 years ago or a few minutes ago. So, how much more so when the transition is to a new body, new personality, quite possibly not human either?
However there are benefits from an open mind about what happens when you die, which is why they talk about past and previous lives. There might be other ways of teaching in the West, where the belief of reincarnation is not so widespread, and it would be a shame if someone felt it was a problem with the Buddha's teachings when really it is not such a central part in a way, not the specifics of how reincarnation happens.
If you are totally sure that when you die, that's it, then the teachings on cause and effect that the Buddha gave are hard to relate to as you only have the short timescale of our life to see them in action.
Also the idea of escaping from the wheel of suffering is going to seem somewhat limited if you are certain that at the end of this life then that's the end of everything.
You can relate to all this still, to some extent, by looking at the short term effects of your actions in your life though.
Also if this life is all that there is, then you may feel that the scope of things you can do is also limited. There is only so much that anyone can do in a single life.
If we have limitless future of some sort, then that means limitless future possibilities. It leads to a vaster kind of approach to life to think there is more to it than what we are aware of in this short lifetime.
But if you have an open mind about what happens when you die, that opens you up to a vaster perspective in time.
I think however that you can also open up to this vaster perspective by thinking about the ripple effect, that by relating to things in a more sane, clear fashion, without self deception, that helps others around you, and that helps others and so on out in space and also to all future time.
Possibly you could be a Buddhist and follow the teachings and have this vast feeling of the Bodhisattva just through relating to those ways of thinking, I don't know. Seems at least possible.
However is probably a benefit to think about ideas of reincarnation to help to be more open minded about what happens when you die, whether or not you believe them. Can you disprove them, can you prove your own views on the subject? It might be good to think through that if you do have a fixed idea that e.g. when you die, that's the end of it all.
Scientists certainly are not at all clear about how mind and body relate. Especially obvious in Quantum Mechanics where the idea of an observer is not clearly understood at all - what it is that leads to the "collapse of the waveform", why we see things in particular places and times.
Some scientists do believe that when we die, that's it. But plenty of others believe in reincarnation or in an after life. All those views certainly seem to be compatible with science as it is practised by actual scientists.
So it doesn't seem you can prove it one way or another by the scientific method at least not on present day understanding of science. Which is also incomplete, there are many things that we don't know, our present day theories are a fudge, with many hidden constants not explained, and with QM incompatible with General Relativity - relativity explains how space curves but can't explain the matter that curves space, and quantum mechanics can't explain what happens in situations of strong gravity - and also quantum mechanics itself is not thoroughly understood mathematically, the so called Renormalization problem
So, are plenty of reasons to suppose that the science we do is at least somewhat limited in its scope and the things it can answer.