Yes for hygiene reasons and to avoid a rash you should wipe using either a wet wash cloth or an adult wipe or even baby wipes.
Wipe the pee off when you change your wet adult diaper because the pee that is leftover on your skin can lead to a rash.
However if you prefer to just put on a new adult diaper after changing the wet one then plan to take a shower a few hours later then it shouldn't be a problem.
After giving birth I wore adult diapers for temporary urinary incontinence and would wipe every time I changed the diaper just like I would wipe my babies diaper area when changing their wet diaper.
The pee can lead to rashes.
Make sure you're changing the diaper every 2 to 3 hours or when it gets full enough.