The actual saves are not converted, just the game, so you will not be able to continue with the same character after installing the conversion patch.
If you do not have FoV yet, you can continue with your existing character until the end of D2:ED, then
upgrade to Divinity 2: Developer's Cut and re-create your character at the beginning of FoV (level 35). You wouldn't have the same equipment (though you'd probably be upgrading that fairly soon anyway) or various loot (which is replaceable), but can match the character's appearance, skills and stats. Battle tower servants are chosen randomly with a new FoV character, but there are other NPCs in Aleroth to perform those functions if you don't like who you get.
If you have FoV, you can wait until you finish the game with your current character, and then get the full upgrade to the Developer's Cut (which would be much easier if you ever need to reinstall the game, rather than installing D2:ED and then FoV and then the conversion patch).
Being a free upgrade for those who bought the PC versions of D2:ED/FoV/DKS (see link above), the copy of D2:DC from the
Larian Vault (or directly through Steam, for that version) pretty much makes this conversion patch obsolete.
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