Another risk... has a re-write been brought-up before and shot down? Did everyone agree (reluctantly) to make the best of it and continue with the code base? If that happened and you bring this up again, it may not end well. Management may see it as you undermining the project, not "being on board", etc.

So unless you feel really compelled to do this, and you can do a good, objective quantification (here is why a re-write will make us more money) as why it must be done, don't bring it up.

Also, telling mgt that a whole team in the company produces bad code may not be in your interest and it certainly won't make that team your friend going forward.