Short answer to your question: Yes.
Clicking on children will not work because it is inside a button. The button is not intended for a container for children - only for text.
Try it. You will find that he will always tell you that you pressed the button.
<button type="button" onclick="alert('You clicked the button!');">
<p onclick="alert('You clicked the p!');">Hello</p>
<a href="#" onclick="alert('You clicked the a!');">Hi</a>
</button>
Demo
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