The open source distribution does support sending out via HTTPS using the HTTP Sender. However it just uses the default Java truststore, so any custom certs you trust will have to manually be added to cacerts. Advanced options like hostname verification, mutual auth, etc. aren't supported with the open source distribution.
The SSL Manager extension expands on this, adding TLS support for all socket-based source and destination connectors:
- DICOM Listener / Sender
- File Reader / Writer
- HTTP Listener / Sender
- TCP Listener / Sender
- Web Service (SOAP) Listener / Sender
- Email Reader / SMTP Sender
It not only enables TLS but allows advanced fine-tuning options on a per-connector basis, like Hostname Verification, Mutual (Client) Auth, tweaking protocols / cipher suites, and more:

On top of that it provides a one-stop shop for all trusted and local certificates / keypairs used across your server. You can even create entirely new certificates in the Administrator, generate a CSR, and import the reply from a CA.