Not necessarily. Raising interest rates lowers inflation.
So increasing interest rates is a double-whammy on housing. The increased mortgage prices lowers home values, fighting inflation _AND_ causes future profits to be discounted (relative to the risk-free bond rate).
The housing market was overheating earlier this year because low 2.5% interest rates meant that people's monthly payments were much lower than people expected. But now that we have 6% mortgage prices, the monthly mortgage price is increasing (which will eventually force housing prices down).
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This is why rising interest rates is the main tool of the Fed right now. Its not the perfect solution, but its sufficient until Congress enacts lasting change (ie: policy changes that lead to an increased supply of our luxury goods). The bank can only change interest rates so much before it becomes unreasonable.