There is some uncertainty in my opinion. First, as far as I know, we do not have experimental evidence what happens in long term under UBI. (The existing experiments were too limited in time and scope.) Second, I am not sure how much I understand the factors behind land/house costs, but I assume that Georgism is approximately correct, and that the obstacles against building more homes are more legal/regulatory than economical. (Which means that a change of law could change the situation on the housing market.) I assume that the reason for rising costs is simply "not enough houses" so the people auction for the existing ones, and the reason for not enough houses is that it is legally difficult to build them in sufficient amounts.

If the following is true, then pouring more money to economy simply means that people will have more money to auction against each other; that is, the costs of housing will rise. (Like, if 1200 families are fighting over 1000 houses, and new houses cannot be built fast enough, then even if you made all of them billionaires, ultimately some of them would not have enough money to buy a house.) But it is not obvious how will this interact with UBI. Maybe the prices will rise just high enough that you cannot afford your own house on UBI alone (or on UBI plus the average wage), and then they will stop.

The regulatory reasons against building more homes are the following: First, people who already own houses in the city, do not want every remaining piece of grass in their neighborhood to be replaced with new houses, so they will elect politicians who vote against this. Second, there are rules saying that a house must have at minimum a certain number of square meters, etc., which on one hand sounds like a good rule that prevents horrible homes from being built, but on the other hand it also puts a minimum price on a home, which some people can't afford. (From the average voter's perspective, it is a choice between a good house and a house that sucks. From the homeless person's perspective, it is a choice between a house that sucks and living on the street. So if voters remove the "house that sucks" option...) Plus there is an interaction between these two effects; people who already own houses in the city also do not want a lot of "houses that suck" to be build in their neighborhood, because it would mean that a lot of poor people (e.g. former homeless) will move there. Also, there is a zero-sum game between those who already own houses, and those who don't -- higher costs for the latter mean more profit for the former.

To provide affordable living for everyone, you would need a combination of "build a lot of new homes, even if it means many of them are small and uncomfortable" and UBI. Only after you built enough homes so that everyone can have one, then their costs will stop growing; and only then people will be able to afford one on UBI alone. -- The question is, whether the government willing to enact UBI will also be willing to build a lot of cheap homes. It sounds reasonable, but there will be strong lobbying against it.