I get the sense this question about finite bound on ADC measurement time, isn't really about ADCs or comparator application circuit design, but rather a concern about metastability and system noise (error voltage), and their impact on life-critical/medical applications.
Although all commercially available ADCs work -- trust me, really they do -- I recognize you're trying to simplify your design for some kind of life-critical product medical design review. It sounds like the real crux of the problem is how to prove that a design has acceptable mitigation against metastability in the digital input synchronizer. This question has seemingly veered in different directions though, first about ADCs and the well-known problems of digital metastability, then 1-bit ADC circuit... I'll try to answer both questions here, but you may get more useful results from this community if you rephrase and ask the question again with a title that references metastability, e.g. "life-critical application proof: metastability and digital input synchronization". Although this kind of question does come up sometimes, I've never seen how the medical/life-critical system proof is normally addressed -- what little I've seen has to do with ensuring that the medical device cannot harm the patient. Must be answerable though.
Mitigating Against the Possibility of Metastability
The remote possibility of metastability cannot ever be completely eliminated in any digital system, because it's physically impossible to switch between logic low and logic high voltages without slewing through the intermediate 'gray zone' that provides the noise immunity, inherent in a digital system. The best defense is to slew as quickly as possible, and use multiple stages of flip-flops when crossing clock domains. This doesn't make digital logic itself impossible or unreliable, it just means careful design is required to ensure correct operation.
The commonly used practice is described several places, such as this related question: Synchronising GPIO transitions to an external clock
Check the medical regulatory standards that your device needs to meet, as this should tell in objective, measurable terms what is an acceptable risk.
Comparator + Voltage Reference = '1-bit ADC'
In the comments, I suggested using a standard comparator + voltage reference as effectively a 1-bit ADC. This is a well-known technique. At the risk of being a shill, here's one of the integrated comparator + voltage reference chips that my employer offers: http://datasheets.maximintegrated.com/en/ds/MAX9025-MAX9028.pdf . See figure 3 for the optional external hysteresis circuit. Not trying to push Maxim parts here, it's just that's what I'm most familiar with.
A comparator is very similar to an operational amplifier, but optimized for low input offset voltage, large differential input signals, fast output rise/fall times, and fast recovery from output saturation, to switch quickly between "logic high" and "logic low" output levels. Most comparators also use open-drain output instead of push-pull. The synchronizer metastability issue doesn't apply to the comparator itself, but obviously does still apply whenever an asynchronous signal enters a synchronous digital clock domain. So the customary digital input synchronization techniques should be used at that point.
The 'finite bound on measurement time' is known as 'propagation delay' (tPD+ and tPD- depending on rising or falling output level). This propagation delay depends on the input overdrive level and the supply voltage. See for example MAX9025 Typical Operating Characteristics graphs at the bottom of page 7 of the data sheet. Since this device has typically 4mV of internal Input-Referred Hysteresis, the input overdrive must exceed this hysteresis level for reliable detection. From the Propagation Delay (VCC+5V) graph (MAX9025toc27) the propagation delay is less than 40us. More importantly, the Rise Time (1.6us typical) and Fall time (0.2us typical) are what determine the fraction of time that the output can spend in the 'gray area' that potentially could trigger a metastable state. These are given in the data sheet as typical values because of the dependency on system capacitance.
This Analog Devices article provides a good general introduction to how to design a hysteresis circuit around any comparator.
http://www.analog.com/library/analogdialogue/archives/34-07/comparators/ Note especially the noise shown in figure 1. Without hysteresis, analog noise is captured as digital noise near the switching threshold. Adding hysteresis shifts the effective switching threshold by adding a small amount of positive feedback.
Temperature itself is one source of noise -- Johnson-Nyquist noise affects all electronic components to some degree. Even if your circuit were cryogenically cooled with liquid helium (presumably at high operating cost), there would still be some small amount of thermal noise. How much noise, actually depends on how long you measure it. Sometimes this is specified on op amp data sheets in units of V per square root of Hz. Usually this effect is considered negligible.
Temperature variation is another source of noise, as most every component has a temperature coefficient. Mismatched temperature coefficients cause a system to have some degree of sensitivity to ambient or operating temperature. When the HVAC system turns on and warm or cool air is forced into the room, there can be a small but detectable variation in measurements. Whether or not this matters in your application, I can't determine.
If you haven't already, your next step should be to contact an applications engineer at one or more of the companies that make analog ICs. System-level design review is really the only way to address your concerns about medical regulatory compliance, performance, reliability, and cost trade-offs -- this is beyond the scope of what can be answered here.
I'd suggest you start with (in no particular order) Linear Technology, Analog Devices, Texas Instruments, Maxim Integrated (my day job) -- these are the big analog companies I'm most familiar with, but certainly not the only IC manufacturers that deal in op amps, comparators, and voltage references.