****rron plate chiller and immersion pre-chiller?

A recent post of a similar nature made me start questioning my cooling
setup. I have a ****rron plate chiller.  Here in Virginia, the tap
water is around 80F (give or take a couple of degrees) during the
summer.  I also have an old 50' immersion chiller that I pretty much
no longer use.

Would it do me any good to use the immersion chiller submerged in an
ice bath as a prechiller for the water going into the plate chiller?
Or should I continue my present method of just cooling as much as I
can with the plate chiller (mid 80s) and crash cool in the fridge
until I hit ale pitching temps (low 60s).  This usually takes a
several hours...

Thanks in advance - M