The output of U1 will follow the noise from U2. In other words unless the signal output is also referenced to U2s output (5V), the signal output will simply follow U2 as referenced to ground and you have no Common Mode Rejection when ground referencing the signal output.
A simple thought experiment will show this, with no signal input U1 output is @ U2 voltage (5V). If you change U2 to supply 6V (think of this "change" as "noise"), then U1 will follow to 6V output, likewise if U2 changes to 4V, then U1 follows to 4 volts.....so no rejection of U2 "noise" is present!!
If you must to use this configuration, think you'll need to use a very low noise reference/regulator for the 5V.
Best,