No, not at all. Only the rear body mounts had to be lifted to accommodate the later shock mounts. I used a '69 semi-auto IRS chassis with a clutch tube welded into the tunnel.
However, that was the '56. Many years after being "restored" I found that it had been done badly with non-original parts. That's not to say it is beyond use but that the heater channels and valances are wrong for the year. I was tempted to get it all redone and then at the VolksWorld show last year I was offered a near-perfect 54 shell and chassis for 1/2 the cost of the repairs so I grabbed it.
The chassis I am now using is the '54 but with IRS diagonal arm mounts welded into the rear forks.
Here's some pics of the 56 on the 69 chassis....
Edited to say - oops just noticed the first pic is of the SA chassis