More than likely not. Unless, as CraigB mentioned, you have a Multi-Device subscription. For the pro version of Avast Mobile, the subscription is $11.99 USD per year and the lowest Windows OS version subscription package is $59.99 USD per year.
Just that alone tells me there's no way it would apply to PC unless the devs overlooked that.
I would say the $59.99/year option is actually worth the cash. Real-time and online protection is a must for Windows PCs with how often you can and will run into malware/attacks. No matter how careful you are online, it can and will happen. I learned that the hard way, recently.
However, if you feel comfortable with the free version of Avast for PC, stick with that. Avast is one of the best free security options for PC. From my experience, most other free anti-viruses are a file scan tool with subpar definitions.
Hope this helps.