Most boils do go away without draining.
Usually within 1 to 3 weeks a boil even when not drained should go away and heal up on it's own.
If the boil lasts longer than 3 to 5 weeks then you might want to drain the boil or get the boil drained by a doctor.
You can put a warm compress on the boil several times per day to help promote draining and healing of the boil.
The last time I had a boil on my skin the boiled drained out and healed on it's own after 2 weeks so the boil should heal within 3 weeks at most.
Eventually though the boil will heal whether you drain it or not but getting the boil drained may be the best option if you don't want to wait for the boil to heal on it's own.