Basically the bill zeros out the transfer and making taxes for suppressors as well as removing them from the definition of a firearm under the NFA, which is part of the tax code. The GCA of 1968 still lists suppressors and suppressor parts in its definition of firearms, which is in a different section of the Code of Federal Regulations. So suppressors and suppressor parts would still require a 4473.
But since this is a reconciliation bill, Senators can challenge provisions that they don't think are related to the revenue under the Byrd Rule. If the Senate Parliamentarian determines they don't qualify, it takes 60 votes to overrule. Lowering the tax to zero should qualify, but removing them from the definition of a firearm in the NFA may not survive. It does have a chance, however, since the NFA registry is the mechanism for collecting the tax, and the methods by which taxes are collected can be modified within running afoul of the Byrd Rule.