Answer

Yes — in Jain tradition listings, Shree Shantinath Bhagwan’s Nakshatra is Bharani. ( jaintirth.in)

Explanation

Jain panchang uses nakshatra as one of the factors for choosing auspicious timing for rituals. So Bharani can be seen as a special and favorable time for Shantinath puja / aradhana. ( jainknowledge.com)

If you mean “should Shantinath puja be done only on Bharani nakshatra?” then the answer is no — that is not a restriction. Bharani is a special association, but darshan and puja of Shantinath Bhagwan can be done on any day; Bharani is mainly used for special observance or extra devotion. This last point is an inference from the Jain panchang usage and the nakshatra association. ( jainknowledge.com)

Spiritual Understanding

For a Jain devotee, the main purpose is bhakti, purity, and remembrance of the Tirthankar’s qualities. The nakshatra helps in sacred timing, but the true value is in the inner भावना and faith. ( jainknowledge.com)

Takeaway

Bharani = special nakshatra of Shantinath Bhagwan. Puja can be done any time, but Bharani is especially शुभ for His worship. ( jaintirth.in)