^No you don't.
The benefit of a hydraulic tensioner is that you can replace the bearing down the road when it goes bad instead of the whole tensioner. Some E39s came with hydraulic tensioner while others came with mechanical ones.

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00 E39 DINAN S1 //M5 (82k miles)
06 E53 DINAN 4.8iS, born 2/18/2006 (126k miles) http://www.xoutpost.com/bmw-sav-foru...s-my-dslr.html
90 Straman Z32 TwinTurbo Convertible, (1 of 44 ever made) 5 speed, 444rwhp/451rwtq
01 360 Novitec Spider F1 (26k miles)