CallManager does not support H.323 Fast Start in either direction. It will not send fast start calls to H.323 peers, and if it receives a fast start call from a peer, the call will fail back to H.245 (slow start) negotiation, so that peer must support this.
I think this is planned to be supported eventually but I don't know when or in what version. There are a few corner cases of special features that CallManager supports that makes implementing fast start "interesting." For example, let's say you have 2 phones sharing a line appearance, and one phone is in a G.729 region and the other phone is an a G.711 region. Now a fast start call comes in from an H.323 peer that is trying to call that shared extension number. There are some other interesting scenarios, but again this is not supported right now.