Importance of Providing PAN Number
If you do not provide your PAN number, you will not receive credit for the income tax deducted from your salary. Why would you want to lose out on that? Additionally, you may end up having to pay higher income tax on your behalf, which is a situation of concern.
Legal Actions Based on Appointment Letter
On another note, yes, they can take action based on your appointment letter. However, the most they can do is request notice pay, minus the amount owed to you for the days you worked but were not compensated for. It is not economically feasible for any company to pursue legal action in such cases as the legal fees would surpass the recoverable sum. Your defense could revolve around the fact that you were not paid in a timely manner, which would be a violation of the implied clause in the appointment letter. Nevertheless, I am skeptical whether they would proceed with any legal action.