Running Chrome on an AWS micro instance
AWS gives you complete control of the OS so what you're suggesting makes sense.
The main disadvantages of running a GUI over the network come down to bandwidth and latency issues, so you might want to consider getting an EC2 instance as close to your region as possible.
Keep in mind AWS Security groups, which will need to be configured to allow your VNC connection.
Micro Instances aren't really made for production use, so you may find it's not really a true test of a typical system. You should factor this into your test as it may be more appropriate to use a small instance type.
Other than that, sounds like a reasonable solution.