If you don't have the submitted paperwork, yes. If you do then they generally won't bother with it since it shows intent to keep legal.Even just owning the stock can be considered "constructive possion" by the ATF.
That means that if they can, they will try to prove that by owning the stock without an approved tax stamp, you are planning to make an unapproved sbr in violation to the law.
It doesn't happen often, but if they wanted to, they could, and would pursue it and if convicted it is a felony.
Just having it in your possession, even if never mounted, can trigger that charge, if they choose to.
Personally, I don't trust the ATF at all so, until the law changes, and I believe it will down the road, I follow the letter of the law.
It's just not worth risking the consequences.
Kind of like having a receipt for renewing your car registration. Even though you don't have the registration certificate, it shows intent to renew and payment so you're good to go.