[chongli]

Yes. If the Sun somehow instantly collapsed into a 1 solar mass black hole, it would have no effect on Earth's orbit. The Schwarzschild radius of a 1 solar mass black hole is a bit under 3km, so the event horizon would be 3km in radius. For comparison, the Sun's current equatorial radius is about 696,000km.

To fall into the former Sun black hole would be much more difficult than falling into the Sun as it is now. You'd pretty much have to make a deliberate effort to "land" on the event horizon.