hello aspirant!
hope you are doing
To start with answering your question, ICAR- Indian Council for Agricultural Research examination provides admission to only agricultural colleges all over india. so no you can no get bvsc course addmission under icar exam.

To get admission in veterinary colleges at all india level, a student has to qualify AIPVT examination conducted by Veterinary Council of India.
One can also give various state level veterinary examination conducted by state government of their respective state.
For more information please visit
https://medicine.careers360.com/articles/aipvt