The quick answer is, no. There is no easy way to check for price changes for UV (aka FV) cabins. You have to call Celebrity or your TA to find out. If all 4 UVs are booked, there won't be a price for you to compare yours to.
We've booked the FVs for the past 20 years and it's very rare for us to get a favorable price adjustment after booking.
They are nice cabins, though.