HR Culture and Resignation
All these depend on the HR culture of the organization. Normally, if a person is asked to resign with an offer of notice pay, they will not initiate termination from their side. This is because termination shall always lead to unpleasant situations for the company. Termination can be challenged by the employee when it is not as per the procedures laid down by the law. Therefore, under normal circumstances, the employer will not terminate an employee but will ask the employee to tender resignation. And there will not be any written communication for this. In your case, they have offered two months' salary also. It should be understood that they will pay it and relieve you.
Risks of Immediate Resignation
Is there any risk in accepting the resignation and relieving immediately? Yes, there is a risk. The relieving letter will have the resignation date and the relieving date. When you have the same date or a date of one or two days, it would give an impression that you were asked to go by the employer. When you go to a future employer, the certificate of service or the relieving letter issued by this employer could be read as "relieved immediately, without allowing to serve notice period," and they can ask you why you were relieved immediately without notice. You can say that the project in which you were working ended and you wanted to move to some other organization, but in between, you needed time or space to breathe, etc., and therefore, you requested early relieving and they did so. This would be a satisfactory answer if you have an offer in your hands, but not convincing for all the HRs.
So long as you are okay with the above, there is nothing wrong in submitting the resignation. After all, if the employer does not want you, why should you remain there?