Pull ups are diapers, and you can absolutely get rid of them. Here's the schedule we use. Limit fluids after 6. Potty right before bedtime at 8. Carry to the potty at 10:30. This is how we've been doing it for a year with our daughter who is now 3 1/2.
Accidents will happen, but not very often. Put a plastic cover under the sheet, and keep a big towel handy. For a small accident, just put the towel over the sheet.
If you can pee in a pull up without interrupting your sleep, you may never learn to wake up when you need to pee. But if you pee in your sleep and then find that you're all wet, chilled and uncomfortable, and you have to get out of bed while daddy or mommy cleans you up, you start to develop the awareness that you need.
Now, nobody wants their child to have accidents at night, but my daughter is much more likely to wake up to pee if she needs to every once in a while. I'd say she is fully potty trained at 3 1/2.