@RenToyonde:
Oh, totally. But a very different sort of bad sign, "this relationship may not get off the ground", as opposed to, "a small red flag right off the bat for an unhealthy, controlling relationship".
On a lesser and more subjective note, since he was the one who asked her for a date—especially as it's not a "first date" in the "we're dating now" sense, iirc, more like "will you be my prom date" tentative courtship stuff—being impolite about her disinterest seems kind of presumptuous to me. If the other person isn't really having a good time of it,
demanding they give you their attention seems incredibly selfish to me. To be clear, this is all entirely down to tone taken: One can tactfully ask, or express a preference that there might be no chatting on phones during dates in general, and so on, without one-sidedly dictating the terms of engagement.
...I sound like some sort of relationship advice column now which is a poor joke given my life; I swear the examples were just to help explain where I was coming from.