No. Its virtually impossible to increase turbo lag on the stock turbo ( if 29.5psi at 2850rpms is lag, then you may need a V12 truck engine ). Now... If this were a realistically sized turbo from the factory ( say... K04 ) and you went from our stock cooler to Deadhooks, then you may see a slight bit increase in lag ( but it would still be crazy worth it ), but with our stock turbo, ford pretty much has the car fighting as hard as it can to CREATE lag on purpose. The reason for this is many ( longer driveline life, tire life, fuel economy, emissions, engine/rod life, octane limits, drivability as far as smoothness).
Most people not used to the insane "mis-match" involved with a turbo this small will say things like that. Even if you read some old school turbo books, it will say the samething. But in this application, almost no intercooler is too big. The little stock turbo just pumps out so much heat, and it spools so hard, so fast, that even if it did increase lag, it would worth it ( which it won't ).
I went through the same thing with my equally mis-matched stock turbo on my srt4. I had the same idea as your friend. I was looking at installing a 32x24x4 intercooler on my srt4 ( which is huge ). After I bit the bullet and did it, I was pretty upset that i had been mis-lead by these old school books, and even people posting on the forum posting the same info. Now.... Almost ever srt4 ever has a huge cooler in the front of it. They even did an intercooler comparison that showed the huge ebay coolers beating the pants off smaller high dollar coolers. If you want to dig through it, i posted a bunch of info on this in 2J's race intake thread ( I don't have the time to find it ).
Bottom line is... No, lol. Not the case on this car and this turbo. And if you have a bigger turbo, your already making most your power in the topend, so either way, a giant cooler is the only way to fly.