No, Destructive Devices, Machine Guns, etc. don't have to be "Registered"--they have to have a TRANSFER TAX paid to posess them.
Technically, the MG (DD, SBR, SBS, AOW, etc.) is listed in the NATIONAL FIREARMS TRANSFER REGISTRY (actually a tax log).
Still one of the most screwed up things the Gov.org came up with--for you to get an NFA item, you have to submit paperwork, get fingerprints, a CLEO signoff --just to be sure you are eligiable to pay the tax.
And, they set the $200 tax ($5 for AOW, if only because one Legislator of the time had the balls to stand up for something) at the value (at the time) of a Thompson SMG.
The idea was that 'gangsters' used them, so if they doubled the price, the gangsters wouldn't get them--so, the average joe now couldn't afford them, however the rum runners (and Irish Whiskey smugglers--you know how your family got their money, don't you Ted Kennedy!!) had plenty of $$ and had no trouble buying the guns.
It is also my understanding that live (Explosive) 40mm shells are individual destructive devices and need to have a $200 transfer tax paid on EACH shell (Damn expensive shooting).
AFARR