Is it possible to have a current account without a savings account? If it is possible, then if the client withdrew more than of its balance, how will the overdraft occurs?
I'll assume you are in the UK, where 'current account' is the normal term for what is called a 'checking account' in North America. By that I mean an account where you do your day-to-day banking and which allows you to write cheques, withdraw cash with a bank card, set up automatic payments etc.
Not only is it possible, it's absolutely normal. A current account is usually the first thing you set up with a financial institution. In fact many institutions won't let you set up a savings account without a current account. The only case where you might be forced to create a savings account to get a current account is with a Building Society (Credit Union to North Americans).
Overdrafts are generally unrelated to savings accounts. If you take out more than is in your current account, you owe the bank money. The bank will not normally transfer funds from a savings account to 'top up' a current account (though it can sometimes be arranged).
I'm not sure what you mean by a "current account"? Checking?
If so, the answer is that if you don't have an overdraft fallback set up -- which may either be drawing from the savings account or drawing from a personal line of credit -- the check bounces. (Which usually means your bank charges you a fee AND the vendor charges you an additional fee...)