Yes-No question in 2AFC staircase test
Lets introduce some notation. Lets $S_i$, with $i = 1 ,2$, represents the different stimulus classes and $R_j$, with $j = 1, 2$, represents the different responses. In a one-interval task$^1$, $S_1$ is presented half the time and $S_2$ is presented half the time. In a typical two-interval task, stimulus $U_1 = &lt;S_1,S_2&gt;$ is presented half the time and and  $U_2 = &lt;S_2,S_1&gt;$ is presented the other half.

The responses $R_1$/$R_2$ can be yes/no, a/b, up/down, or anything you want and it does not matter in either the one or two interval cases. In the two interval case, it is just as valid to ask did the first interval contain the signal: YES -- NO? as which interval  contained the signal: 1 -- 2?

With a transformed staircase, you might run into problems. It is not clear exactly what you are proposing to do. If you always present $U_1$, or present $U_1$ half the time and $U_2$ the other half, then the response that causes you to increase the difference between $S_1$ and $S_2$ would always be $R_j$ (with whatever $j$ you arbitrarily choose based on your labeling of the responses). To get around this you could present some catch trials with $&lt;S_1, S_1&gt;$ and maybe even some $&lt;S_2, S_2&gt;$, but what happens if you get unlucky and get a bunch of $&lt;S_1, S_1&gt;$ trials in a row. You will likely keep reducing the difference between $S_1$ and $S_2$, but that is strange since the signal level is not relevant in the catch trials.

While you can probably get away with it, there are likely better procedures/methods (e.g., dual pair comparison)

$^1$ I study audition so am used to talking about temporal intervals while sometimes in vision multiple stimuli are presented across different regions of the visual field. From a signal detection vantage, it doesn't matter.