Yes, If your FFL is a sole proprietorship no ATF form 4473 is required. You can simply log the firearm out to yourself. Keep in mind that there are rules for selling or transferring these items from your personal collection (see below).
No, If your business entity is any other type (e.g. a corporation, LLC, or partnership). An ATF form 4473 and a NICS/Background check are required for everyone, including the officers of the business and the responsible parties.
As stated in an ATF newsletter dated September 2013 (#8 Page 3).
“Yes. If your business is a sole proprietorship, no ATF Form 4473 or NICS check is required to transfer a firearm from your business inventory to your personal collection. However, the acquisition and disposition (A&D) record must reflect the disposition of the firearm from business inventory to personal use, and the date of such transfer. Please note that if you wish to dispose of the firearm prior to it being held as part of your personal collection for one year, you are required to re-enter the firearm into the A&D record, complete an ATF Form 4473, and conduct a background check on the transferee. However, if the firearm is maintained in your personal collection for one year or longer from the date the firearm was transferred from the business inventory, you are not required to comply with the provisions of §478.102 or 478.124. Reference27 CFR 478.125a.” link