Answer

If you mean a Śvetāmbara Terapanthi layperson, then generally yes—you can do Navanu Yatra as a pilgrimage, but it should be in a way that fits Terapanth principles. Terapanth rejects image worship, while Navanu Yatra at Shatrunjaya/Palitana is a temple-based pilgrimage that normally includes darshan and other ritual actions, so a strict Terapanthi would usually avoid the image-worship part. ( jainpedia.org)

Explanation

Navanu Yatra means the 99 ascents of Shatrunjaya, and it is regarded as a major Jain tirtha-yatra. Terapanth is an aniconic Śvetāmbara tradition that does not worship images and places strong emphasis on fasting, ascetic discipline, and meditation. So, the pilgrimage itself may be undertaken, but the ritual style matters. ( sahapedia.org)

Spiritual Understanding

In Jain Dharma, the real purpose of a yatra is inner purification, restraint, and devotion. For Terapanth, that devotion is expressed more through self-discipline and meditation than through idol worship. ( jainpedia.org)

Takeaway

So the simple answer is: yes to the yatra, but not in the mūrtipūjak ritual form. ( jainpedia.org)