Not really, you can use DNS to point YouTube.com to an iP you control, but the problem is that you will get TLS issues. It won’t redirect the hostname, but just the IP address. You could use a custom CA and sign YouTube.com certificates, but you will likely still have problems if you use Chrome because they will be pinning certificates for Google services, and your mobile applications will also pin the certs so your mobile YouTube will stop working completely.
I would set up an Nginx container to forward all request to youtube.com to your ViewTube container. Then in PiHole set the A record for youtube.com to be your Nginx container.
If you don't use Vimperator I recommend checking it or any other tool that allow you to get more control of your browser, especially if, like me, you spend most of your day in it, not on your desktop.
No, pihole won't help you there because what you want is nothing a DNS can do, you need a proxy server to handle that. How this works depends on the proxy server you are going to use.