Down here, we call that "Fringe Dwelling"...

A "Texas Wedge" is another name I have heard used when a player reaches for the "flat stick" when not on the putting surface...

I have seen a guy make a sand save out of a bunker with a putter.

So, no, IMO a putt from off the putting surface is just another stroke and doesn't count towards your final PPR stats.

We don't like fringe dwellers down here...

They tend to pinch the drinks on medal days in the putting comps...

Cheers