definitely - if they're not pressure-sensitive, your son will have no way of learning how to vary his volume. Dynamics are a huge part of music, so this is really crucial.
::looking into electric pianos::
Well, if you're looking for a really nice, high-end electric, the Yamaha Clavinovas are great...but very expensive (far upwards of a thousand dollars). I think what you're looking for is more like
the Yamaha DGX505 Portable Keyboard. This is a very good, 88-key electric piano by Yamaha, listed at about $550. Keyboards like this, by Yamaha, have built-in a large variety of different sounds, so that hitting the key can sound like anything from a flute to a gunshot, and a lot of rhythms, so that you can have a looping background rhythm to play to.
Other than that, though, I wonder why you're looking for an electric at all? I like electrics, no doubt, but I can't say that I've ever played on an electric piano that's as good or better than a real piano - it always is off a little, in terms of feel if not tonality.
If you decide to go for an acoustic piano, I'd recommend Yamaha, Kawai, Sohmer, or pretty much any upright piano you can find for about a thousand or less. Don't necessarily shy away from a piano that's made by a company who you don't recognize; if you like the way it sounds, buy it! In the end, the name doesn't matter at all compared to how it sounds and plays.
I have to say that, if an upright piano and a grand piano sound the same, then there's no need to get the grand - a choice that i had to reluctantly make about a year ago, and opted not to spend my parent's money on a grand.
The difference between a grand and an upright that sound the same isn't worth the difference in price tag.
Good luck piano-hunting, and tell us how it all worked out when it's settled!