Negative, CIC cannot/don't ask for account balance as that will come under breach of privacy, moreover banks are not allowed to disclose details of a person's account.
What I have read and heard that during bank verification, they basically look for below informations, and they ask questions indirectly.
1. Whether the letter is issued by bank or not.
2. Authencity of signatures and seal.
3. Confirmation of Name, address, phone number of bank as mentioned.
However CIC gets suspicious if the amount mentioned on bank letter head is suspicious.
For ex: If the amount mention is ₹6,50,000, this will raise suspicion as majorly the account balance is upto 2 digit past decimal, for ex: ₹ 6,51,376.66.
I have read an incident wherein an applicant photoshoped $1500 to $15000 which was suspicious, the applicant got banned for 5 yeras.