I have a doubt on W2's. Now my friend who is an employer is not able to File the W2's online with SSA due to some problem. But they have to give the W2 to their employee by Jan 31st. So can they issue a W2 to the employee without filing the W2 Copy A with SSA?

Yes, at least initially.

The IRS does NOT get access to the SSA's database until September at the earliest; that is why the IRS wants a copy of your W-2 attached to mailed tax returns and the data contained in the W-2 to be imputed on electronic returns.