You should.

I run a Deuce Factory sway bar in the rear and feel that it contributes a lot to my 32 roadsters good handling.
Especially so on twisty mountain roads.

The DF sway bar is small and fits most Model A, Deuce style cars with no problems.

When I had the sway bar disconnected to replace the bushings, I was surprised at how much the body would rock when you gave the roll bar a couple of good back and forth shoves.

Not so with the sway bar hooked up.

I haven't driven it without the sway bar nor do I want to.

Roy Fjastad of the Deuce Factory commented in one of the rodding mags a while back that they'd found a rear sway bar was sufficient in the A's & 32's and a front sway bar was not required.