If it's already that damaged, it would be better to pull it first. Old flooring should never be covered if you don't know the condition of the sub floor. Especially if some of it is water damaged. Additionally, by adding a layer prior to your new finished floors, it can affect door jambs, thresholds with other floors, etc.

I've done remodels where I've pulled 4 layers of flooring and aside from the nightmare, it's always because the prior installers (or owners) didn't want to do the job properly the first time.