Yes, LVT pushes prices down. A 100% LVT on a property with a present land value of $1M won't collect $1M in taxes every year, it'll depress the price until the amount in LVT is at a low enough level that someone's willing to pay that to have the property.

High property prices aren't axiomatically good, if that's what you're going for, and the fact that people spend millions on construction as well suggests that sometimes properties are worth more than their raw land value. People will be able to make a ROI for the actual productive investment in building and maintaining property, even if speculation and economic rent are cut off.