The old days:
In the old days people thought that electrons are just like little spheres, that occupy well defined positions in space and have well defined momentum. They thought that they could apply the Newtonian laws of mechanics to an atom and workout, in detail, properties such as energy, momentum and position etc like they did very successfully with the planets moving around the sun.
These efforts failed miserably, however, as the results of the calculations gave answers that made no sense when compared with the experimental results. The discrete energy emission by the hydrogen atom could not be explained or produced by the laws of Newtonian mechanics. So there was something wrong about the assumption that electrons must behave like little balls.
To make things worse, Davisson and Germer did an experiment in which they fired electrons against Ni crystal and, to their astonishment, they found that the way electrons pass through the crystal is very much like light (X-Rays) pass through a crystal. In other words the electrons displayed wave behaviour! This result was reconciled with the notion of waves, from earlier work done by De Broglie, who had proposed that matter, in the form of particles, should also display wave-like behaviour. Therefore it become obvious that the ideas of particles with well defined position, momentum, energy etc were not supported by the experimental evidence.
All these indicate that:
No, electrons and all other particles of nature cannot be assumed to have well defined position and momentum prior to a measurement or interaction.
The modern days:
The development of Schrodinger equation, which encapsulates the old Bohr theory of the hydrogen atom and de Broglie's hypothesis, gave an excellent account of all of the observed behaviour of matter, and therefore we have come to realise that we can only talk about probabilities of finding a particle at some position in space. Indeed, we can only talk about the probability for any event happening. Even for electrons in an atom we cannot say that they occupy discrete positions as they move around the nucleus and that they have well defined momentum.
Despite this, the results of our calculations agree with the observed behaviour of particles extremely well!!
In conclusion: Electrons do not occupy well defined positions in space, and they do not follow well defined paths as they go from A to B. As an electron moves from A to B, it does so without following a particular path, so it cannot be in a particular position at any time. The electron , can only be represented by a probability wave, and follows a multitude of paths with varied probabilities in order to go from A to B. If we do our calculations by ignoring some of the paths because we might think they are impossible, our results simply do not agree with observation!
Hence the electron is not teleported from A to B, it is simultaneously everywhere, including A and B.