Do you have to register firearms at all in your jurisdiction? Or is buying one thru an FFL sufficient - and waives going to the local police with the gun to have it entered into their books?
If you don't have to have the gun inspected by your LEO's and recorded, you don't really have it registered. And there is the crux of the issue. An FFL only records a transaction required by law, that a completed gun, or in this case, a lower with serial number, is passing thru his business as legally required to transfer it to the owner.
That's about as much "registration" as goes on.
When you purchase an 80% lower, it's not a firearm, nor does it has a serial number to even note. It can be shipped directly to the owner's residence without passing thru an FFL - which is the entire point, as the cost isn't a major advantage. Blemished lowers are on the market for $39, most 80%'s I've seen are $80 and up with a jig to finish extra.
The attraction for some is the complete avoidance of any record that the lower is in the owner's possession. However, the closing of one vendor and confiscation of their sales records doesn't support that in a positive way. There are other methods that do ensure the lack of government oversight - like buying a lower thru a private seller.
Once the lower is finished and can readily accept a lower kit with trigger, it then becomes legally a firearm and the rules of selling one apply. Don't think that it means the rules that a major licensed producer apply, tho - the BATF is fairly clear on that. It's the large licensed makers who are required to serial number their product and sell it thru other licensed dealers or directly to the public. They have to follow the regulations, the individual citizen does not follow under those rules. What some buyers will insist, tho, is that you do, and provide a "number" to expedite their future transfer.
Registration, tho, no, not so much, not unless every person in your area has to march down to the police station and inform them of their purchase - or completion of a lower. Which I seriously doubt is required.
And, to add, it's better to build it first as a pistol. Don't attach a stock, go shoot it, then be happy. If you build it and use it as a pistol first -which many SBR users do - the firearm enjoys the distinction of not be a rifle first - because if it is, it then will always be a "rifle" to the BATF. But as a pistol, it can become a rifle and then back to a pistol, no regulations prevent it at the Federal level.