If the IRS requires you provide the a copy of your W-2's they will send you a letter. So it is best to wait and see what the IRS will do before amending the tax return. They may process your return regardless of the forms not being included.
It will be at least 4 weeks before the status of your mailed tax return with a refund will be available on the IRS website - https://www.irs.gov/wheres-my-refund