My first post here..I am also from Tijuana Mexico, and I use a combination of ice surrounding the pot, cold water and some ice cubes inside...this ice cubes are from a bag I got from the around the corner store, so it is sanitized....my batches are 5 glls, so my question here, is, does this changes the OG drastically?
It is generally a bad practice to add ice cubes to your wort as they can pick up bacteria while freezing. Usually something settles in an ice tray or there is something in a commercial setup, etc. OK to eat, but leaving it in a sugar solution for a week with yeast can cause a bad batch of beer.
As to your question. your OG should be calculated to a given volume. So if you use extract, and are suposed to start the ferment at 5 gallons, then adding ice and water to a partial boil til it gets to 5 gallon you should be fine. I'd still be concerned about ice and it possibly carrying bacteria, but other than that, as long as your final volume is about what you were supposed to have, adding water or ice wouldn't change OG