I do not know if Synapse can, but Indy cannot, at least not directly.
Indy uses OpenSSL primarily, and you can access the Windows certificate store yourself to export the desired certificate(s) and then manually import them into OpenSSL's certificate store. Or IIRC, at some point in time there was a 3rd party effort to integrate the Windows certificate store directly in OpenSSL itself, so you might try looking around for that patch.
Or, you can write your own custom Indy SSLIOHandler class to use Microsoft's SChannel API instead of OpenSSL, then it would use Windows certificates transparently.