No, letting your Azure account lapse or not enabling MFA (Multi-Factor Authentication) will not affect your Visual Studio license or installation. Visual Studio and Azure are separate services, even though they are both under the Microsoft ecosystem. Your Visual Studio license is tied to your Microsoft account, not specifically to Azure.
However, if your Visual Studio subscription includes Azure credits or other Azure-related benefits, you might lose access to those benefits if your Azure account is not active. But as far as your Visual Studio installation and license are concerned, they will remain unaffected.
If you don't plan to use Azure, you can simply ignore the MFA requirement for Azure, and your Visual Studio will continue to work as usual.