Close Grip/underhand Grip are very different, training-wise, than wide grip overhand. Imagine benching with a wide grip, then benching with a close Grip underhand. Both chin variations will train your lats, but we’re talking a MUCH more forearm/bicep/elbow heavy movement, in return for a less strenuous shoulder movement. I just do lat pulldowns with an overhand grip to make sure I get the effect. Truth be told, I think lat pulldowns are better for hypertrophy than wide grip pull-ups.
In short, yes- switch up your grip, just don’t expect the same lat dominance during them. I bet you’ll get nice and sore right behind your armpits the day after you first do them, though. That’s the nice thing about variations. If you do underhand though, be wary of the forearm/wrist pain that can happen after a while - I’m one of those people who can’t do the wonderful straight B.B. curl because of it, I need the ez bar- it flares up if I do too many in a week.