2k warmup? Depends on how cold it is outside I guess. I suppose mine will start at 2k, but it'll drop to about 1300 real quick, unless it's about 40*F outside. But I don't let it idle for more than 10 seconds or so (especially in cold weather) before taking off nice and easy. The car warms up faster if you drive it gently and load the motor, driving helps keep oil pressure up, quicker you get it up to operating temp the more efficiently it's running, etc. Some people disagree with this, and that's okay, this is just my philosophy.
I think you mean "surge" when you say "search"
I've been keeping a close eye on my car for a while now. Its been 250 miles since i replaced my 02 sensors and cat, and my car is in Ready status and there's no pending codes. So I think my emissions and CEL woes are behind me. It's been a warm day today (~75*F high), and I noticed at one point my car was idling at around 950rpm with no load. It did this twice as I was in traffic and its the first to happen though I've set it to idle at 650rpm (+/- 25rpm). But no, once warm, it should just idle at 600-700rpm smoothly unless something loads the motor, like the AC compressor engaging/disengaging, thermostat opening and closing and radiator fans turning on/off, etc.
Necessary fix? Depends. My car would shut off after a while of driving and have issues starting up unless I let it sit for about 20 minutes. Its dangerous to have a car just shut off on you while you're driving. Get it fixed.
Can you bypass it? sure. You'll have a running car, but it won't be running efficiently; it'll run rich. You'll possibly ruin your spark plugs, foul your 02 sensors, ruin your cat, and wasting gas. It'll drive and do so as dependable as if it were running, with a few caveats.
You can block the IAC. To do this. Just take the IAC hose off and put bypass caps on the throttlebody Inlet and the IAC outlet. You don't even need to unplug the IAC or remove it with a block off plate, and this will save you trouble from having to reroute the coolant.
You'll probably have to adjust your idle a little higher. Factory is 600-700 RPM, I had to set mine to 800-900 RPM to get it to idle smoothly. It'll still bounce a little, maybe 100 rpm deviation or so. Also, when you lift off throttle or have a sudden drop of RPM (like throwing the car in neutral and letting the rpm drop from 3k to idle), the engine will definitely drop below your set idle, so you got to make sure your idle is high enough that the motor can catch this quick enough and not stall out. With the AC on, my car would stall out every now and then, but I had no trouble with the AC off. If I was going to keep this setup, I'd have to raise my idle to about 1000-1100 to make sure I didn't stall out with the AC on. The IAC helps detect load on the motor (ie: AC engagement, etc) and will bypass air to help keep the motor from bogging down and stalling out. Without it, you've got to manually compensate by raising idle RPM.
Word of caution though. I bypassed my IAC with bypass caps for about a month deciding what to do with the car. This will cause your car to run rich since the IAC is not functioning properly (air metered by VAC isn't agreeing with O2 sensor output, not enough air). The ECU sends a PWM (signal) to the IAC telling it how much to open, thus letting extra air into the intake manifold. Knowing there's this extra air going into the manifold, it adds more fuel. Since you're IAC isn't really bypassing more air through, you're going to run rich. This will foul plugs and the O2 sensors upstream in the manifold, and probably ruin your catalytic converter. Also, if you have an OBD II car ('96,'97), it'll throw an IAC CEL after about 50 miles of driving. I'm not sure if a CEL will be thrown on OBDI ('93-'95) cars, as people removing their IAC altogether didn't have a CEL. After fixing my IAC issue, I had to replace my O2 sensors and my cat had shown signs of overheating from burning rich. My MPGS droped to 22-23mpg when I typically get 25-26.
So if you have to pass emissions upon your safety inspection, you're gonna need this IAC working (or apply for an emissions waiver).