With those old games balance is usually an afterthought. So, do resource controllers actually speed up resource income? More importantly however, does it matter in campaign? As I've learned the hard way on mission 3, you shouldn't build up your fleet too much, or the game will punish you with more enemies. So, it's probably better to keep a hefty reserve RU at the start of your mission, so the rate at which you collect RU doesn't matter, since the real bottleneck is your unit production time. Feel free to correct me, I've barely started the game.

Yes.

The main thing controllers do is prevent Workers/Harvesters from spending thier time flying around rather than collecting.
So maximising the time spent harvesting and minimising the turn-around time to drop of resources.

They're fairly cheap so they aren't a huge investment either for the benefit they give.
Unlike the next smallest ship capable of accepting resources: The Carrier.
If you already have a Carrier though and aren't planning on using it for anything else, using that as a resource base instead of a Controller is a really good idea since it can defend itself/build more Workers etc.

Controllers were far more important in HW1 where your mothership couldn't move and you were forced to go out and harvest far away, and had either build controllers or deal with huge income lags.
In later games they're less important, but still useful.
Shoutout to Cataclysm and it's unique 4-pad version that enables some very fast collection.