No, they will stop buying US Treasuries. Who wants to put money in a currency that is losing value and is paying little interest?
That's a popular notion and might even be right.
On the other hand: A decent sized rate cut might already be priced in to the currency markets.
If the interest rates go down, then the dollar goes down, and foreign investors will be loathe to invest in our equity markets... they would have to subtract the %loss in the dollar from every percent gained in stocks.
But if rates are left alone, the dollar will still go down, because many of the oil producing countries are switching to do their business in Euros. And again, with the dollar falling, foreign investors will not want to invest in our equity markets.
But if rates are increased, more homeowners with be caught upside down in their mortgates, housing starts will fall even more, which will stall the economy, which will bring down stock prices.
Ergo, I think the stock market doesn’t have much upside for the next year or so.