Not when the covariates are standardised though (if you do with the above model x = (x - x.mean())/x.std():
At least in the only likelihood approach you can show that the correlation matrix between the slope and intercept has off diagonal terms that equal to -\frac{1}{n}\sum_i x_i, which when centered is 0. From a geometric perspective if your line is passing through the origin, a change in slope does not result on change in intercept unlike a line not passing through the origin.