Yes, if you employer will not do what is required of them. The Form 843, along with your copy of the W-2 and the document showing the RSU (if necessary) from Employer 1 showing the excess withholding of social security tax.
The IRS will go after Employer 1 for the tax.
Note: When one employer withholds an excess, it's impossible for them to pay that excess amount to the IRS based on the way the employer form for withholding is completed (Form 941). The form uses a formula and not the exact amount of withholding actually taken from the employee.
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