The first one sure, the second one you're still a ways up from the noise floor. A 50 ohm source in <50kHz BW (100kSps) has 0.1uV RMS noise, or ~2 LSBs out of 24 bits at 1V reference. At 2.5MHz, the noise rises to only 0.7uV RMS, whereas 1 LSB out of 12 bits at 1V reference is a whopping 250uV.
ADCs in the 50MSps range and >= 12 bits tend to run into a noticeable noise floor.
Worth noting that the sampling aperture matters; the analog bandwidth of the ADC itself. Even if the source is carefully filtered, if the ADC is presented with a resistance at all frequencies, it's actually sampling at its analog bandwidth, not its intended bandwidth. This is a good reason why some ADC coupling networks recommend an RC filter / terminator at the ADC input: it gives a low impedance, and therefore low V/rtHz, for frequencies above the intended bandwidth.
Put another way, an ADC with 500MHz analog bandwidth (so, well suited to equivalent time sampling and SDR applications), is always reading 500MHz of bandwidth from a resistive source. Even if it's sampling at only 10MSps or whatever.
Consider the statistics: there are effectively more trials (~1 every ns) for the resistance to generate a new noise value v[n] = e_n * rnd(), and the ADC is simply sampling one of them every so often. Doesn't matter how often you sample, it still has the expected amplitude e_n.
Another way to think about it: it is doable in principle to measure the RMS value of any signal, with exactly one sample -- because, what is the expected value (RMS) of that sample? Well, it's the RMS, of course. The error bar just happens to be atrocious (1 point does not, a representative sample, make!). More practically speaking, as long as your sampling is uncorrelated to the signal, and the sampling bandwidth includes the signal bandwidth, then you can compute RMS from those samples, with the the usual statistics (i.e. an error on the order of 1/sqrt(N)).
In any case -- the magnitude of these LSBs, and noises, gives you the template you need to evaluate the performance of a design. Presumably, you should ensure coupling from digital signals (a few volts) to the ADC is in the < -70dB range (for 12b). That includes ground bounce and other EMC relationships. PSRR needs to be similar, and if it cannot be obtained from the opamps/ADCs themselves, then filtering is needed to ensure supply noise is similarly attenuated (whether the reference noise from a linear reg, or switching). Then PDN analysis applies, and optimization can be straightforward.
Tim