Yes, it is absolutely possible! An epidural is optional with an induction, and many women will opt to "see how it goes" and often surprise themselves!
An induced labour is not necessarily a horribly painful event, and in my practice, I am yet to have a woman be induced and request an epidural.
Important factors are one-on-one care from a known and trusted midwife, a strong belief in the natural birthing process and lots of strategies for a drug-free labour and birth.
For more on labour and birth options, Dial a Midwife