The answer is ‘yes-no-maybe-perhaps’.
There are numerous inputs to the price of housing and interest rates are only one of them. Supply and demand, the condition of the national, regional and local economy, job growth or loss, inventory, taxes, rent levels and of course, interest rates — they all go into the equation. But generally speaking, as rates rise and the cost of borrowing money increases, prices tend to either increase more slowly or even pull back.
But as 2004 to 2007 showed us, prices can rise even when rates are rising.