Answer

Yes. There is clear Jain historical evidence from Kumbhariyā in Kachchh that Vādi Deva Sūri of the Bṛhad-gaccha officiated the consecration rites of the Neminātha temple. A second inscription at the same site may also point to Devācārya of the Bṛhad-gaccha. ( gsawb.gujarat.gov.in)

Explanation

So, while Kachchh does not seem to have been a major center of the Bṛhad-gaccha, it was not absent from Kutch entirely. The evidence we have is mainly connected with the Kumbhariyā temple complex. A broader study of Bṛhad-gaccha epigraphy also notes that its inscriptions are found more often in Rajputana, Madhya Pradesh, and Bihar than in Gujarat, which suggests its stronger historical spread was outside Gujarat. ( jainqq.org)

Takeaway

In short: yes, at least some Bṛhad-gaccha monastic activity is attested in Kutch, especially at Kumbhariyā, but the surviving evidence is limited. ( gsawb.gujarat.gov.in)