If I got a notice to quit in 3 days and I vacate the property before the 3 days will I still be sued? What happens next

Whether you will be sued depends on whether the landlord can recover what you owe from the security deposit. But if you vacate within the time limit, then you will not be subject to eviction.

If you have unpaid rental and/or if the unit requires repairs, the landlord can take what owe out of the security deposit. If that is not enough to cover the amount you owe, the landlord can sue you for the balance.