SR 1 and 2 are on different engines so that won't happened. In SR TT we have character customization that is little bit like playdo. I want real human proportions to make my MC the hottest and sexiest as possible. BTW Volition fix the damn female lips in cut scenes
If 2 games do have different engines, technically they still could do that, as long as the character creation/clothing options are similar.
The clothing and character wont be exactly the same as SR2, but they would be their SR3 equivalent.
What they could do is on Saints Row 2 have an Export option, which is basically a file with a list of 32-bit values, each keeping track of different parts of the players outfit.
For example, here is an example template for caps:
00000000 XXXXXXXX XXXXXXXX XXXXXXXX
template for shirts:
00000001 XXXXXXXX XXXXXXXX XXXXXXXX
template for pants:
00000002 XXXXXXXX XXXXXXXX XXXXXXXX
And every so many bits can control a different part of the item, for example:
HAT | HAT TYPE | FORWARD/BACKWARD | HAT COLOR | HAT LOGO | ON/OFF
They could divide the bits however they want, each set of bits representing something different, determined by the exporter/importer
The computation that converts an outfit to a file containing all of these would be inside the DLC Exporter on Saints Row 2. Then it would send it to their server under your gamertag or w/e, and you can Import it with the DLC Importer on Saints Row 3 which would then convert the values back into an outfit.
In Lehmans terms: They could set aside values that represent different items in the outfit, make it a code, export it from SR2, import it onto SR3, it will convert it back into an outfit.
The only thing is, not all of the clothing that exists in SR2 exists in SR3, so they would need to bring back some of the old clothing onto SR3. And body size was controlled differently (if you want the plastic surgeon effects to carry over, they would have to be similar on both games)
They probably did the same exact thing for exporting/importing pokemon from gen 3 to gen 4 and gen 4 to gen 5.
Moreover, its not too difficult to make a similar character from your SR2 game to your SR3 game, so I don't think they would go through the trouble of making this option. Again, it wouldn't be an exact copy of your character, so it would save you just a little bit of time since you can probably remake your character within 5-10 minutes