What are you referring to ?    Did you have the EIC on your originally filed return?    Or are you or will you be eligible for it when the IRS corrects the return for the unemployment exclusion ?  

I believe that I will be eligible for the additional

EIC when the Unemployment is corrected.

Stop and WAIT for the IRS to process the original return.  If you had EIC on the original return then the IRS will recompute that credit as well.  

If you did not have EIC on your return and you are single the IRS will also add the EIC to the return automatically.

However if you have qualifying dependents on the return and was not eligible for the EIC on the original return then WAIT for the IRS to send you the new form 15111.  Filling in and returning this SIGNED form to the IRS as instructed in the notice  so the credit can be added to the already filed return.  This will save you from having to amend the return later and wait another 6 months.