When flying the Captain Sim 737, I don't use the FD, I just use the AP, and that includes using the AP to track the ILS and GS. It works just fine for me doing it that way.
Like most aircraft, it's best to come in on as shallow an angle as you can (if your flight plan allows it) when ligning up with the ILS, as it gives you the best chance of a good fast alignment. Having said that, I can still capture the ILS and GS from wider angles (around 70^o), but it might "chase" the ILS a bit before aligning properly.
Note. The AP will follow the GS before capturing the ILS if you select APP, while coming in from either side of the ILS.