Yes, Chrome (and google) can track that you are using two accounts from the same computer.
Since Chrome is an application on your computer, there is a great number of ways that you can be tracked including:
- some kind of cache
- registry
- any kind of fingerprinting mechanism
Just youtube (or any other Google website) has the possibility of tracking you in a great number of ways, including:
- Canvas fingerprinting
- WebGL fingerprinting
- Fonts fingerprinting
- Installed plugins
- User agent
- OS + resolution
- IP Address
- DNS Leak
- WebRTC Leak
- Any combination of the above
- many more
See Panopticlick (https://panopticlick.eff.org/) or Browserleaks (browserleaks.com) to get a glimpse of what can track you.
Now, even though they CAN, it does not mean that they DO.