As long as you have calibrated your rocksmith and your pickups aren't super low output to begin with, you should be able to get decent note recognition for tapping. The most important thing to notice is how cleanly yout tap the note and do the follow ups with pull offs and hammer ons. If your muting and/or fingering technique is poor, you will easily get accidentals from other strings and even sympathic harmonies from open strings, if you don't cover them while tapping. The accidentals and feedbacks are only more and more audible with active pickups.
The best thing you can do is play with a distorted amp (preferrably outside of rocksmith, due to its noise gate) to see how clean your single string tapping and legato techniques really are. if you are constantly in a situation where your signal distorts heavily, then it means you are doing a poor job muting the strings. If you don't have access to a dirty amp, then tone designer from rocksmith is your friend.