The rejection of ADF test can indicate the covariance stationarity?

I am curious that if the ADF test indicates the time series data has no unit root, can we conclude that the time series is stationary (time-invariant mean, variance and covariance)?

Here is a small example. First we generate a white noise sequence with different variances in the first half and second half. Then I pass the white noise through a stable first order filter to get the output.

Matlab code:

e = [randn(500,1);2*randn(500,1)];  % white noise
F = tf([1 0],[1 -0.5],1);           % stable filter with root 0.5
y = lsim(F,e);                      % output