That's a stretch, I think. Poch has yet to prove he can sign good players and then integrate them as required. His only really notable transfer "wins" have been Alli and perhaps Alderweireld, if you look beyond fitness issues. Wanyama maybe? Who else? Dier? Wimmer? Sissoko? I can't see how you say that he'd have made better use of money when he's not demonstrably done so in the past. He has now had two transfer summers where he's been asked to build from a position of strength.
He may have had lower spend caps, but he's not proved his ability to strengthen the team in the market - so I'd say that the jury remains very much out on that count and to say that history (recent, at that) suggests he'd have made better use of the money than Jose is a massive leap, at best.