How does the 3.3V line withstand that high of an overvolt? Also, if you are thinking about using an unregulated single cell Li-ion with this, that's not exactly wise; after a charge, a 3.7 battery spikes to ~4.2-4.5V, which I know is far too high.
Technically the amp draw should be lower, but if it's not spec'd to go that high it might not.