No, if your developer membership expires, your apps will no longer be available on App Store. However, your app will continue to function for people who already downloaded it.
As the Apple developer program membership FAQ puts it:
What happens to my apps on the App Store if I do not renew my membership?
If your membership expires, your apps will no longer be available for purchase and will not appear in search results on the App Store. However, if you renew your membership after it has expired, your apps will be available for purchase on the App Store within 24 hours. You do not need to resubmit your apps.
You can read more from Apple's membership FAQ, here: Apple Developer Program Renewals FAQ