The HP12 & HP18 I've tried did not have the typical Islay peatiness as exemplified by the likes of Ardbeg, Lagavulin, Laphroaig, et. al. It does have a pleasant honeyed smokiness that is very well balanced. I went back and did some more digging and even though some of the malt used by Highland Park is peated to 35-40ppm, the resultant new make is about 2ppm (need more supporting references for backup, but here's one for now):
In short the answer is "NO", HP does not have the Islay peaty flavor profile.
[EDIT] - Please ignore my initial post regarding peating levels as that was an incomplete picture of the mashbill.
Also, this is slightly OT but found some interesting videos about Orkney Peat put out by Highland Park: