Would I ride that frame around town? Yes.
Would everyone criticize me for doing so? Yes.
But IMO aluminum frames are more durable than people think; I have happily ridden aluminum builds on the street. You'd pay more than $600 for a Pista anyhow. If he had bought the bike NEW for $1500 I might say keep it track-only. But it is used and affordable.
Should he ride it around on the street? Well, I guess that depends on how good he is at cycling. I'm gonna give him the benefit of the doubt though and say he isn't ********.