I was told I could apply for a visa to China at a Hong Kong Travel agent (CTS). Can I leave HK airport to arrange a visa while transfering there and then pick it up n my return?

Yes, you can apply for a China visa from CTS and pick it up on your return. There is a CTS at the Hk airport. There is no need to go to the ones in the downtown. Also, five hours are not enough to travel to and back from the downtown.
But one thing is that when you submit your passport and other requirements to apply for China visa, how can you enter other regions without a passport?