I want to remove the dot above the "i" in Illustrator but still keeping the text as an editable vector object, is this possible?
Right click your text and select Create Outlines. This turns your type in to "an editable vector object" which you can select with any of the selection tools and delete the dot above the "i".
I suspect what you meant though was keeping your text as live editable type. In which case, no you can't do that. Theres no way to edit the path data of a font in Illustrator whilst keeping it as editable type. You could cheat and hide the dot above the "i" by using a clipping mask, you would need to adjust the mask every time you edit your type though.
Another thing to keep in mind... There is a dotless i character. Check to see if your font has that character. If so, problem solved.