Amazon only syncs purchases and files sent through the Amazon service. It pushes them down to your Kindle software on various platforms. The kindle software on your PC does not push files up to Amazon or other devices.
You can email personal documents to your Kindle. From Amazon support:
With Kindle Personal Documents Service, you can send your personal
documents to your registered Kindle devices, supported Kindle reading
applications, and your Kindle Library in the Amazon Cloud through the
Send to Kindle application or your Send-to-Kindle e-mail address.
There is a fee for this service:
Fees for the Kindle Personal Documents Service via Whispernet are
based on the size of the file submitted (before compression if you use
a .zip file), your country, and where you're accessing Whispernet.
Personal documents service fees will only be charged for documents
that are successfully delivered to your Kindle device via Whispernet.
Personal documents service fees are rounded up to the next whole MB
and apply to each personal document delivered via Whispernet to each