I'd say the inverse is more likely. If you're going to fire a single request to a domain only you are using and you're running a full local resolver, it may make a difference.
For a public CDN: your browser already has the file cached. If it doesn't then it has the domain cached. If it doesn't then the dhcp-provided resolver has it. If it doesn't, then at least it already has the TLD nameserver available immediately, and the TLD can serve that response from very hot cache. It's CDNs job to make sure this happens.
With a vanity domain, you can fully control the TTL values. All my sites use a vanity domain because it doesn't tie me to a particular CDN, and they have 86400 TTL.
When you have a vanity domain like cdn.example.com, the recursive resolver already knows the nameservers for example.com, so this actually reduces the additional DNS lookups.
I'd say the inverse is more likely. If you're going to fire a single request to a domain only you are using and you're running a full local resolver, it may make a difference.
For a public CDN: your browser already has the file cached. If it doesn't then it has the domain cached. If it doesn't then the dhcp-provided resolver has it. If it doesn't, then at least it already has the TLD nameserver available immediately, and the TLD can serve that response from very hot cache. It's CDNs job to make sure this happens.