Depends upon the type and conditions
A direct acting will only if the pressure upstream is less than the set point
Most diaphragm operated pilot controlled globe valves (Cla or equal) will open unless there is a return check feature in the piping or a power chamber type has a disconnect between the two disks.
If you really need a large backflow for a (larger) pressure reducing valve, you should consider a needle regulation valve. A high-priced, but very flexible solution for a large span of pressure and flow. Can easily be modified or guaranteed for backflow.
Note on needle valves: Yes, price is high, but lifetime could be very long without any service at all. In addition flow capacity could be high, and a smaller valve with abrupt flange extension could under circumstances be used. Specialist consultation is necessary for dimensioning.