I don't think so. A set of conductors or each set of conductors is allowed to be connected to the transformer secondary without OCP as specified in the following sub-sections 240.21(C). Not connected to a wire 5 feet away from the secondary, but 'to the secondary'.
And then there is the fact that you cannot supply a tap through a tap 240.21.
Taps won't have an AIC rating, but they will have a Short Circuit Current Rating (SCCR) and this rating must be equal to or greater than the available short circuit current at the point where they are installed. There are connections with high SCCR ratings available.
There are accepted tables that show the withstand of conductors based on the fault current and the clearing time of the OCPD.
Power distribution blocks are considered suitable for use on circuits having available fault current not greater than 10,000 rms symmetrical amps,
unless marked with a larger value. Power distribution blocks are marked
??Short-Circuit Current Rating?? together with the value of the rating and the
maximum voltage. A power distribution block may additionally be marked
to identify an overcurrent protective device (fuse or circuit breaker) to be
used ahead of the power distribution block.