Answer
Yes, such experiments can be carried out.
Work Step by Step
The electron has a dual wave-particle nature, according to the complementarity principle. So the electron will exhibit interference and diffraction effects in an experiment with 3, 4, or many slits. With a grating, the interference fringes will be much more pronounced, as they are in experiments with light.
The uncertainty principle will not be violated. The electron locations are better known (smaller $\Delta x$), but their momentum is not as well known (larger $\Delta p_x$), because there is a larger lateral region for all of the slits that the electron could have passed through.
The Heisenberg Uncertainty principle for matter will still hold, $\Delta x \Delta p_x \geq \frac{\hbar}{2}$.