Is it possible to design a digital filter to remove the ripple in the passband,
In addition to the difficulty that Hilmar mentions, just pertaining to finding a filter, if you try this you'll find that a real analog filter also varies from part to part, and over temperature, aging, etc.
So if your need is critical, and you're designing for production, you'll find that some of your systems will work nicely some of the time (when the filters match what you designed to, because of part variation and environmental factors), but none of your systems will work all of the time.
You can get around this by choosing more precise components in your analog filter, but that's expensive, and introduces supply-chain difficulty. In fact, the general trend in this area has been to just sample faster, use a "looser" analog filter, and possibly put that really nice anti-alias filter into the digital realm, right before you down-sample the signal internally.
potentially even correcting the roll-off which will occur all the way to the stopband?
Probably not. Generally the analog to digital conversion process introduces quantization noise, which is spectrally flat. Trying to reconstruct the signal when it's been severely attenuated means amplifying that noise along with the signal -- you'll just end up with lots of high-frequency noise that's masking your high-frequency signal.