If I install a small air compressor/engine, generator, and tank in my garage, and I charge it up at night when electricity costs $\frac{5.4p}{kWh}$ and use it during the day to power my house when electricity costs $\frac{12.5p}{kWh}$ would this be able to save money on the electricity bill or not?

The tank, engine, and generator should be sized to charge up over 7 hours between 01:00 and 08:00 and release the energy during the other 17 hours of the day. I'm assuming that regardless of when during the day the energy is actually released it is either used by me or goes back into the grid and runs the meter backwards to offset my day-usage.