Will putting a new tire on a bad rim cause more vibration then the old tire with less tread?
replace the rim at the same time. you will save yourself a great headache.
Will probably cause less vibration if mounted correctly and balanced but why ruin a new tire with a bad rim and start to have the same problem (again)?
if the rim is bent that alone will cause a wobble as it wobbles you are wearing out all the suspention parts and risking loseing traction on a slick surface possibly causing a crash if its bent change it if its rusty so much that your tire leaks air that would be bad also