Let's say I run arduino on 9V DC buttery and my pedals are powered by 9V DC switch adaptor.
Can I still connect grounds together?
I once tried to make a common power supply for a collection of five peddles for my son, to replace all the batteries. The result was that two of then went up in smoke.
It turns out that they have what is known as earth lift resistors in place to cope with common grounds on the signals. There was not a common power ground. In the end I had to make five small mains powered isolated supplies, one for each peddle.
So beware trying to power two things off the same circuit. Test first to see that there is a common ground on the supplies.