Okay.
So, the real ISO is actually about 1000. I forget, but Ilford has a PDF of it somewhere (not the regular D3200 PDF, I don't think). However, in a speed enhancing developer, you get to about 1250. This is in comparison to TMZ, which gets to about 1000. This is with densitometer testing.
However, and this is the key thing - Delta 3200 and TMZ are both low contrast film. Just because the ISO standard testing method puts it at 1000, or the densitometer testing of Zone 1 puts it at 1250 in, say, Microphen, doesn't mean that it'll look the best at those speeds. in fact, it will look low contrast, but with better shadow detail.
Therefore, the film is well suited to pushing to at least 1600, and well beyond that. You don't block up the highlights as fast, plain and simple, while you are bringing the midtones up to an acceptable level.
As others have mentioned - why shoot D3200 when you can just push TMY or TXT? There are a number of reasons.
Pushing TMY or TXT to 1600 gives you a contrastier negative, with less shadow detail,b ut also much, much tighter grain. For me, if I'm shooting in a low contrast situation (some wedding receptions come to mind), pushing TXT makes sense to me. The increased contrast actually helps, and yes, the grain is smaller.
However, let's say I'm shooting in a hight contrast situation. Maybe a market at night, where there are really bright street lights spread out all over the place. Then it's better to shoot D3200, even with the expense of grain, because the highlights on people's faces and whatnot will be better controlled.
Right tools for the job. Sometimes it's better to push TXT, sometimes it's better to shoot D3200. Neither, IMO, is right all the time.
allan