No, Publisher verification will not allow you to bypass the admin consent requirement. Some permissions are simply considered "sensitive" and cannot be consented by end users. The same applies for any tenant-wide permissions (usually, any of the application permissions). While there are some controls for tenants to define which specific scopes can a user grant consent to, this does not affect scopes requiring admin consent, and it's not something that you as the application owner can control.
That said, you should still add Publisher verification to all your applications, as Microsoft is marking apps without verification as "risky", read here: https://learn.microsoft.com/en-us/entra/identity-platform/publisher-verification-overview#benefits