Not really - makes zero difference to the stator current; the regulator will shunt more current, however the OEM MOSFET type does not run very hot anyway so not going to make much practical difference
(With an old-school SCR Shunt type, it would certainly make it significantly hotter - but it doesn't have one of those :D)

With a series R/R (SH847) it makes situation better - lower current in both stator & R/R

Just as a comment, someone was concern, in a different post, about locating the series R/R under the side cover. After locating mine in that location I have pulled my side cover off several times after a long ride and laid hands on my R/R. It was warm as expected, but not excessively hot in my opinion. I could continuously hold my hand on it with no problem. It works just fine in that location with no heat issues while it does its thing.
 
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