No, your A1 cannot use the Custom chips on your A1200. Its impossible. The A1 is built on modern hardware and not shackled to the past, the custom chips are too slow and too old for modern software. Most Amiga software benefits from graphics cards, even the old Picasso II beats AGA hands down in speed and colour depth.
You have to use an 'Emulator' such as UAE since it can emulate 1000s of Amiga games successfully.
I have been using Winuae for 3 years and is better than my A1200 ever was. Of course some badly written games sometimes refuse to run, but the majority can.