I voted yes, and in my mind probably pretty emphatically.
One is free to think and do whatever one wants, as long one is ready to accept whatever consequences there are.
However if one devotes oneself to a particular system to the point of identifying with it and 'joining the system' in order to get the results which one is convinced the system will lead to, then that changes things - at least from the perspective of the system being effective or not for you to get the promised results.
To be Buddhist, as has been pointed out above, means to have such complete confidence in the Buddha, the Dharma, and the Sangha that one takes refuge in the Three Jewels. By taking refuge it doesn't imply hiding or simply being protected in a passive sense, it means that we take steps and measures in accordance with the Buddha's system outlined. The Buddha was most clear about cause and effect - whether related to karma or other forces. He was also pretty clear about the nature of mind as being something which has it's own dynamic, which in turn has a bearing on our happiness.
The fact that a Buddhist gets hung up about the "person/self" literally being reborn and not understanding it is merely a continuum of mind is more indicative of the lack of study, reflection and meditation than a case of not being able to prove something empirically.
As has been pointed out above, faith is an important ingredient, and again when the Buddha asks us to investigate his teachings it isn't about determining whether they were true or not but more about 'why' they are true - developing greater conviction, which in turn leads to better results.
If you don't believe in an ongoing mental continuum, if you don't have any conviction about cause and effect, that's ok - but this system is not for you. The whole structure of Buddhism is based on cause and effect (4NT, 8FP) and the ongoing mental continuum.
Meanwhile if one wants to continue investigate, what harm is there in that?