If you have points/condensor, out of adjustment or burnt points will cause hard starting, poor acceleration and a rough idle. A bad condensor will cause basically the same thing. Upgrade to a pertronics unit, you will love it.
not sure what you consider a tune-up. Cap, rotor, points and condenser is what i consider a minor tune-up. Plugs and air cleaner are next on the list followed by wires and fuel filter. Timing can also make the car run rough. Vacume can also cause problems normally highlighted by a fast idle.
A bad cap, rotor or points can make the whole engine run bad, where plugs, cap or wires can attack a single cylinder.
If it has been 20,000 i'de probably get everything. If the wires are looking real good skip them. With a clogged fuel filter the car will idle good but run bad under load and acceleration.
If by Distributor, your referring to the cap, as the previous posts said, It'd idle/run poorly. My parants had a Valiant one time that lost a tooth off the distributor gear. You want to talk about a rough ride.....We nick named it the "Getty Up-Go Car" (Hey we were young). As they'd drive down the road, it'd pause on just about every revolution of the motor, then surge ahead. It's a good thing we were young, because otherwise, I wouldn't have been caught dead in it. It sure looked funny though.