No that payment which is deducted by Banks on 1st Ramzan in the name of Zakat does not serve the purpose nor absolve you from the obligation to pay Zakat.
First as I mentioned above, it does not and cannot be treated as Zakat as the main condition in Zakat is that it should be given to a person who deserves Zakat. The conditions that who is eligible and who is not are quite strict and have to be followed (conditions like he/she should be a Muslim etc), otherwise anything you give out would be classified as Sadqa, not Zakat.
Secondly, whatever amount you have in PLS on 1st Ramzan is usually just a small portion of your total wealth. Zakat is liable on 2.5% of your total wealth (excluding the house you live in and your consumables). So that includes all your other investments, shares, plots, cash, gold, overseas properties etc. One cannot just think that since the Govt has deducted Zakat from his/her saving account, there is no need for Zakat calculation. Do note that Zakat is payable on total wealth of a person each year and not just on profit from PLS.
