Oh looky, her 21 Jump Street ep is on YouTube...
'80s hair!
'80s computers!!
But at least the women weren't wearing linebacker shoulder pads.
(Though it seemed like a fairly daring storyline for the time and the time period
21 Jump Street originally ran. But then, maybe FOX was far more progressive than I remember.)
However, given Depp's barely there appearance in the ep, it doesn't seem like he and KLS would have spent all that much time together - especially when, as was already pointed out, he worked in the studio and KLS worked on location. Although, maybe he stalked her on his own time and at his own expense and/or caught as much of her downtime between scenes as he possibly could.
Only Depp and KLS know for sure...