All correct, apart from all the wrong way round guys If you shut off the idle circuit on a carb when running you're not going to get the correct progression from idle circuit to main circuit
The primary function of the idle solenoid is to cut off the fuel to the idle circuit when the car is shut off to prevent the carb flooding itself and being difficult to start.
The secondary function (not on 1700s) is that it shuts off the idle circuit on overrun to try and aid fuel economy, ie: its open all the time that the engine is running, except when the throttle is closed and the RPMs are above 1400 ish. There is no special relay for this on 1700s its only the 1400 and 2 Litres that do this function. The second connector for this usually goes on the throttle spindle, where it grounds the relay to tell it the throttle is closed. Don't ground this on a 1700 car because the two wires are both switched live (one for the idle solenoid and one for the electric carb preheater) so you'll have nicely fried fuses if you do that
Actually, if I stop to engage brain before posting, you're totally right - it does indeed leaves the idle circuit active when driving normally. I even thought that was stupid when I was typing it....but did it stop me?!
If the setup is the same as for a B14, no, you need to leave the one for the idle solenoid connected, and the wire for the throttle stop needs to be grounded, if it can't be correctly connected. That way the solenoid opens as it should - you just lose the over-run fuel cut feature. I'm 99% sure the CISAC will be the same.
If the wire fell off a few days ago, this could be the cause of your poor running - it's behaving like it has no idle circuit. My B200K never misbehaved like this when I was running the CISAC, but my 340 B14 has done this, and it will (just) run with the solenoid out of action, but it's seriously shakey, will stall when coming up to a halt, and generally run like turd...including being awkward to start. You may find the results are worse still with the CISAC.
Yeah, you can run it provided its the ground wire that's broken, not the 12V. So long as the solenoid is connected and active then you're fine. If you ground the wire to a permanent ground the relay thinks the throttle is closed 100% of the time and you'll get all sorts of running problems.
That's how we ghetto-rigged Nessy and it worked, although I'm guessing it didn't run right on light throttle, as the idle solenoid would have been 'off' above 1700rpm (or whatever it is). More throttle and the idle circuit probably isn't making a sufficiently significant contribution for it to be a problem.
Presumably you need to bypass the control solenoid (i.e. feed the solenoid +12v constantly) to have it work correctly?
Yeah that's how we rigged Nessy at FIRST. Then it wouldn't rev above about 1500 rpm, so I disconnected the ground wire, or more correctly, the signal wire for the relay, that grounds when the throttle is closed.
If you remember correctly, we started it up and it wouldn't rev properly, so I went and disconnected the signal wire cos I'd got it permanently grounded, which was wrong. If I didn't disconnect it at the carb then I disconnected it at the other end.
If you shut off the idle circuit on a carb when running you're not going to get the correct progression from idle circuit to main circuit 
