No. It sounds unnatural. In this case, you can omit sự. I'm not sure about the rule, but sự never goes with hạnh phúc. To nominalize hạnh phúc, you say niềm hạnh phúc. However, it does not fit this case. The word thành công in this case can be nominalize with sự, but can also be omitted.

Same question, got marked wrong for the given answer plus cái.