The labour you experience will still be very much a labour. You will have contractions and your cervix will need to thin and open, to make way for your baby to come down and be born. Fortunately, this usually happens relatively quickly, once the labour is established, with the pushing phase usually being shorter.
Many women seek pain relief during their labour after their baby has died. Often to help them deal with the labour process, or even to 'remove' themselves in some way from it. Coping with the shock, and the uncomprehending pain felt when your baby has died, can be difficult to endure, on top of the pain of labour. Seeking pain relief can also be the result of the speed, and intensity, of an induction, together with the natural speed of a labour usually experienced when a baby has died. However, the baby may be born before you have a chance to use any pain relief.
Any form of pain relief is acceptable, and should not affect the way you progress in your labour. For some reason, it is rare for a woman to need forceps or a Caesarean when using pain relief, (as may be the case if the baby were still alive). Be aware that a narcotic injection (such as Pethidine), may 'space you out'. This could be what you want, or could detract from the memories of the birth you may later wish to cherish. Your caregivers are usually more than willing to provide you with anything (and everything), to help you through the labour. They will guide you, if they think the birth is imminent.
Some women wish to feel, and experience, the birth, to help them come to terms with the loss. In this case, using heat packs, showers and baths may be the tools you need to use, to help with the labour. In reflection, many women have looked back on this approach as a decision that helped them in their grieving process, in the weeks, months and years that followed.