No, mosses do not have secondary growth. Secondary growth takes place in vascular plants. Mosses are non-vascular.

Vascular cambium is responsible for secondary growth in a stem.

Primary Growth adds height, while secondary growth adds Girth.

Secondary growth in cortical region forms secondary cortex inside and periderm outside the cortical cambium

Primary growth is responsible for elongating the plant. In woody plants, primary growth is then followed by secondary growth which allows the plant stem to increase in thickness or girth.