As of Liferay Sync 3.4.2 (released June 15, 2017), users can specify their own certificate store. The ticket describes the problem and solution:
We should add documentation to Liferay Sync's configuration page here.
It should say something along the lines of:
When connecting to a server via https, the following error will appear if the certificate cannot be verified: "The security certificate could not be verified". Choosing "Proceed Anyway" will bypass verification and leave the connection open to compromise.
Liferay Sync will attempt to read the certificates specified in the Java Control Panel (see section 20.4.5). If Java is not installed, users can also put their certificates in [user.home]/.liferay-sync-3/certificates. Liferay Sync will trust all certificates in this folder.