The short answer is no. A static pressure on a piezoelectric will generate a fixed charge on the piezoelectric. PVDF has a high input impedance and in order to read out the charge induced on the piezoelectric an electronic circuit is used. The charge will be slowly leaked out of the piezoelectric due to losses in the system. Any of the piezo sensor sites such as http://www.pcb.com/techsupport/tech_pres.aspx#.Uw35emyYaUk

provide a description of the mechanism for losing electrons

There is similar qustion

https://www.researchgate.net/post/If_a_material_is_exerting_a_pressure_of_1-4_mm_of_Hg_would_it_be_enough_for_piezoelectric_to_produce_output?tpr_view=pmjOvULsZmYqQ5ShVe05oaL7mOWHH6pmS9LO_3

by Henry Savage: "you will have to create a sampling scheme that discharges the piezoelectric charge" . I doubt on this statement. It leads to "perpetutum mobile". Static pressure (without movement) produces electric energy (I*V)

You can measure quasi-static pressure through convoluted sampling schemes, but steady static pressure can't be measured with a dynamic (piezoelectric) system. It's just far easier to use piezoelectric for dynamic readings and strain gage or capacitance for static. We have used piezoelectric materials for static pressure, but it wasn't actually using piezoelectric mode, it was just using the capacitance of the sensing element and the change in the thickness with pressure (and subsequent change in capacitance) to measure static systems.

for Henry Savage: Thank's for Your's explanations.

So, for static pressure You use capacitance mode with external AC-sourse. And what is about sensitivity? (dC/C )/dP Can You give some reference data?

You are correct, capacitance sensitivity is low, but when put into the a Wheatstone bridge-like circuit there is sufficient change to measure pressure. Also, the polymer piezo materials are better as they are more compliant than the ceramics. On a deep sea oil field pressure sensor, we were able to measure depth with capacitance mode and smaller differential oscillating pressure from the pumps in piezoelectric mode.