If he has your EIN he may be able to import the W2 early if you have partnered with Turbo Tax and made it available.

If you are mailing the form and not giving online access and are not an import partner then  do NOT give them that number ... tell them to wait for the form and not to try  file without it.   

If they file before they get the form their return may be incorrect requiring it to be amended  AND  the return will not be processed until your W-3 has been processed ... so jumping ahead of he game will do no good.