I rather doubt it... Firstly, you can still access her Dream Palace regardless of your choice and that location is gated behind Romantic Kas so we know it doesn't affect that. Secondly because it would be very silly to make it possible to lock out a major thing like that for picking the wrong option in a piece of missable dialogue in a technically optional quest; you won't get the option to give Vacia the ring unless you're on the Romantic route and you pick the 'Question' option before moving on when you find the ring.
How you resolve the quest will probably alter dialogue down the line at least, since the game tracks that choice in your save flags.