Yes. But......Normally the agreed deals are signed off by an FD, like any business, I guess that will still be Levy.
I actually think Paratici is going to be of more value in selling players / telling Levy that Sissoko has no transfer value, etc
I doubt Levy is going to give Paratici a transfer budget and say "spend that however you like, my old mucker".
If we think back to the sale of Bale, I'm pretty sure Baldini was under instructions to sign players young enough to have a resale value. If my recollection is correct, ALL the "Magnificent Seven" were early to mid-20s with the exception of Soldado, who'd just scored 20-odd goals for Valencia.
I can definitely imagine Levy laying down strict conditions over the type of signings Paratici is permitted to make with the transfer budget.
Plus woolwich recently fired pretty much their entire scouting department to concentrate on the Moneyball God of Analytics and an operating model where agents approached them with players.
I suspect scouting is a very different game from when Frankie Arnesen rocked up at WHL with his "little black book" & persuaded Levy to sign a fantastically promising young Brazilian CB named Rodrigo Defendi....