What happens if I e-file my tax return on FreeTaxUSA.com without entering one of my employer's state ID numbers?

I worked in two places this last summer, and only got a W-2 statement from one of them. The only documents I have from the other employer are my pay stubs. The stubs I have didn’t have the Employer ID number nor the State ID number.

I was able to find their EID online, but not their State ID #. Therefore, I left that part blank. (It allowed me to continue through the rest of the form.)

If I e-file the tax form now, will not filling out the State ID # keep me from getting my refund deposits? Or will the workers at the IRS be able to find the employer’s State ID # with their federal ID # and still process my refund?