No, if the model isnt available here, it usually wont be possible to replace any parts etc if required, even if you pay for it.
In fact, in warranty, they may somehow make you wait some time and get you a part (IF its international warranty and valid here), but there may be some constraints in there too on part availability. Check the warranty doc.
Once any such warranty expires and if the model isnt available here, they will NOT provide any repair/replacement/service, no matter how much you offer to pay.
Thats why I prefer Dell. Most models are available both places, so service isnt an issue. And international warranty is easy to get and they honor it without any fuss.
PS: I thought the dv3 was listed on hte HP india site? Check up.