The answer is yes but the difference is that when you add the zero, the mean is going to be lower.
For example, if there are these 4 numbers: 0, 5, 8, 9
0 + 5 + 8 + 9 = 22
22 ÷ 4 = 5.5
5 + 8 + 9 = 22
22 ÷ 3 = 7.3
The mean is different by 1.8.
~Hope this helped~