There are two reasons why a modern hybrid car could fail to start due to lack of electricity. Two reasons, because every hybrid car has two batteries (12V and HV).
One is that the 12V battery is flat. You cannot push-start it then, as the 12V battery boots up the computers that connect the relay of the high-voltage (HV) battery. No computer boot up, resulting in non-working motor-generators. No regenerative braking then.
The second is that the HV battery is flat, but the 12V battery may or may not have power. The HV battery is at least in Toyota and Lexus hybrids used to drive the motor-generators (MGs) MG1 and MG2. These together start the engine using the power from the HV battery pack. So, there is no conventional 12V starter motor in these hybrids.
If you have a flat HV battery and 12V battery that is not flat, in theory you could power up the computers of the hybrid car. However, I don't believe any hybrid car manufacturer has added the code paths to charge the HV battery with regenerative braking when the HV battery is flat. It would most likely be a software-only change, but I don't believe the required code lines are there... Most likely it tells you to contact the dealer and refuses to work.
So, the answer is most likely no. If the 12V battery is flat, you need to jump-start it or charge the 12V battery. Push starting definitely won't work as the computers cannot be booted up. If the HV battery is flat, I don't believe regenerative braking would save you, but I might be wrong.
By the way, in Toyota/Lexus non-plug-in hybrids, if the HV battery is flat, only dealers can recharge it using a special charger. Minor garages won't have access to the charger. However, this is a very rare issue, as every line of code in the computers of the car has been written to save the HV battery from charge depletion. If it looks like the HV battery would become empty, the engine is started to charge it. The only remaining issue that can't be solved is self discharge, but that would take months of non-use to cause any problems.
Now, which one is the most common issue? It is definitely a flat 12V battery. Leave the lights on, your 12V battery is flat. Don't replace your 12V battery for 10 years, it will most likely be flat (whereas the HV battery is designed to last the lifetime of the car, i.e. 20 years). Don't drive the car for months, the small constant drain on the 12V battery also makes it flat (whereas the HV battery is disconnected by using a relay).