I strongly disagree.
What you are describing is no different than playing a board game, other than the board is an agreed upon construct of the collective group's imagination. In fact, you can actually directly plot every single element to a physical board and it would not change a single thing. In other words, you have played a game, certainly. But, without any actual attempt to decide your actions based on the persona of the created character, rather than pure pawn play, there is no role being played.
I know people REALLY want to insist that just because there are D&D books sitting on the table, we're role playing, but, frankly it's not true. As I said before, you can certainly inject role play into a board game. I'm sure most of us have done that. Well, the reverse is also 100% true. You can play D&D and, really, any RPG without any actual R. Congratulations, you've drifted a role playing game into a game. There's nothing wrong with playing that way, and, I think a lot of tables play that way, certainly in the early days of gaming anyway.
But, without the assumption of some sort of persona by the players, even if it's not backed up by mechanics, and purely free form, without that assumption of a persona, there is no role playing going on. You're playing a game. No different than being a full back on a soccer field. Yes, within the game, you have a role - full back - and that role has certain rules around it, but, there's no persona assumption going on there. No one is going to seriously claim soccer is an RPG. So, without the assumption of a persona, there is no role play.