Your speculation is interesting, but it is totally misleading, I am afraid. Do not go deep into that.
Your additional remark is rather confused because of terminology:
In addition the potential energy is sometimes defined as capacity of a system to do work. On the other side free energy is defined as the amount of work that a thermodynamic system can perform. Isn't that the same thing?
There, it is "the difference in free energy" and not the "free energy" (like potential, free energy is defined up to an additive constant). And the "thermodynamics system" needs to be in contact with a heat bath in order for your statement to be correct. You can think of free energy as a mechanical potential like gravitation, and work can be extracted from the system by changing the free energy. The difference is: the free energy change includes the heat exchanged with the heat bath.
Note: be very careful with terminology and always read statements of thermodynamics in full, otherwise you will be lost.