If you are the sort of person who would do that Harry will assume that you lie if presented with that evidence unless you also successfully fool Harry as to what sort of person you are (and presumably he will default to not trusting you if unsure). Otherwise you are just wasting your time.
But Harry’s inference will be the same regardless, as the evidence he gets doesn’t differ between,
I flip, get lucky, and tell Harry heads and
I lie and tell Harry I flipped and got heads or even
I flip, get tails, and tell Harry heads.
If you are the sort of person who would do that Harry will assume that you lie if presented with that evidence unless you also successfully fool Harry as to what sort of person you are (and presumably he will default to not trusting you if unsure). Otherwise you are just wasting your time.