The wave function of the electron will collapse, as there is an observer who measures what slit the electron goes through. As a result, the wave function of the electron will collapse. The intensity pattern on the screen will be a particle pattern, computed as follows:
I = I1+I2=|A1|^2+|A2|^2.
Here, I is the intensity, A1 and A2 are the probability amplitudes of the electron going through slit 1 or slit 2.
The observer makes this experiment classical. Without an observer, we would have:
I = |A1+A2|^2=|A1|^2+|A2|^2+2|A1||A2|cos(theta1-theta2), which gives an interference pattern. The square modulus of A1+A2 is because the electrons quantummechanically go through both slits at the same time (superposition principle).