We totally doubt it. This is because of rising yields in the EMU and quite steady long end of the curve in the US. We present the discrepancy on the chart below (green and yellow lines for the German curve, blue for the American one.
We can see that the American curve has hardly changed while the German curve move substantially higher as institutional investors cut their long bunds positions and the current price is closer to its fair value based on CPI.
It is worth to note that if the Fed hikes, it will most assuredly affect only the short end of the curve and low inflationary processes in the US and inflow of capital to the US treasuries is making the long end of the curve relatively anchored. Therefore, we should see some appreciation of the US dollar but not so big that it could push EURUSD down to parity.