Yes, the system will check for the values in the database if the ABBS based on Custom Variables is enabled.It also depends upon how the survey is distributed:
1. Using the tracked link: Then the system will check for the custom values in the database and on the basis of that ABBS works.
2. Using the anonymous link (without the custom values): Then it will work on the basis of the browser cookies if the respondent clears the browser cookies then he will be able to take the survey multiple times with the same browser.
3. Using the anonymous link (using the custom values): For example, if the customs value is present in the survey link (https://www.questionpro.com/t/AOon8Zn1vN?custom4=QPTEST) then, in that case, custom values will get stored and is linked with the complete response as shown in the screenshot: https://prnt.sc/1q0rjvc
In that case, respondents can"t take the survey multiple times with the same or different browsers.