Yes, mostly. Maybe not having ( as in duration) the ball more as much as getting ( for a shot) the ball. If your bigs have enough passing to play motion without being turnover machines, my opinion is that they'll be fine against most press teams. Your whole team is going to suffer TO's against the really good press teams. Press teams with high Ath, Spd, Def, Stamina and decent IQ's.
On a related note, a good PG (A quick look tells me yours is a decent PG) with a good IQ generally doesn't try to force the ball where there is a lot of resistance. Like if an opponent has a stud defender. Things like that are usually what accounts for differences between distribution Vs Shots actually taken.
F. Dickinson looks like a sucky press team to me (weak Ath, Def, Stamina), I wouldn't alter my shot plan based on that team. But that's just my opinion.