Nah. There's a bit of Madonna in Bey. Both of them are well aware of just how much they've accomplished and as a result aren't massively concerned with 'popularity'. Beyoncé will always have her core fanbase (who actually buy her albums) so she'll be fine.
Both of them care a lot about popularity. Why else does Madonna need to be acknowledged by every new popular girl to feel validated. Beyonce definitely cares the most thats why she works so hard at her image. Who else do you know who tries to get pictures off the internet?