Will my European Health Insurance Card still be valid if there's a no deal Brexit?

It’s unlikely that it will.

An EHIC currently gives you access to state-provided healthcare available to residents of EU countries. We don’t expect EHICs will still be valid if there’s a no-deal Brexit. That means you could have to pay for medical costs that would previously have been covered under EHIC arrangements. The Government may still negotiate an alternative to the EHIC.

Whether you have a valid EHIC or not doesn’t affect the cover provided through your travel insurance.