Can I get into the CMC Ludhiana MBBS with a rank of 257?

Yes, you can easily get into CMC Ludhiana with AIR 257. In fact, with such a good rank, you can get into any top 10 medical colleges in India. I fail to understand why you are considering CMC Ludhiana as your only option unless you are a local of Punjab and dont want to move away from home.

 CMC Ludhiana is one of the best medical colleges in the country but unfortunately, it has only 13 seats for non-Christians and also charges fees higher than government colleges.

However, there isn't any guarantee of admission even with this rank because the counseling is conducted by a state health university and Punjab gives preference to its own resident students. You will be considered only If seats are left vacant in the third or extended second counseling.