Based on the information provided in the search results, it is difficult to determine if you can secure a seat at ESIC Medical College, Coimbatore with a NEET UG 2024 score of 381. Here are a few key points:

- The search results do not include the NEET UG 2024 cut-off marks for ESIC Medical College, Coimbatore specifically

- ESIC Medical College, Coimbatore has a total of 100 MBBS seats, with 20% reserved for ESIC Stakeholders, 15% for All India Quota, and 65% for State Quota

- The NEET UG 2024 cut-off will depend on factors like the number of applicants, difficulty level of the exam, and previous year's admission records

- Candidates are advised to fill their preferences during counseling based on their NEET UG 2024 rank

To get a more accurate assessment, I recommend:

1. Checking the NEET UG 2024 cut-off marks for ESIC Medical College, Coimbatore once they are officially released.

2. Comparing your rank with the cut-offs for the ESIC Stakeholders quota, as 20% of the seats are reserved under this category.

3. Consulting the college directly or referring to the official counseling information for the most up-to-date guidance.

Without knowing the final NEET UG 2024 cut-offs, it is difficult to predict if you will get a seat in the 3rd round. Keep a close eye on the official announcements and participate actively in the counseling process to maximize your chances.