Thanks for your all feedback.MP2660 will detect battery as non-chargable/faulty as it applies a charging current and looks for a rise in volts. If it doesn't see that it will stop charging. It will stop charging if battery temp rises above a limit and also if its core temp rises too much.
I don't understand why/how you think user would swap rechargables for primary cells? Build sensible capacity single Li-Ion cell in to start with. Normally primary/recharge option would be AA/AAA Alkaline v NiMH but thats a dead technology route...
I understand your recommendation ! As per your suggestion there is no need of extra mosfet between mp2660 & battery and if user insert non rechargeable battery mp2660 initially start charging and then if temperature rises and voltage across battery is not increasing immediately it will stop charging with fault indication. So there is no safety concern even if non rechargeable battery is being charged unintentionally. May be i have to think this very good idea.
In additionally i found very low Rds(on) P channel mosfet which is having less than 10mOhm Rdson. If charging current is 150mA so there is hardly any voltage drop across the mosfet . And this not change mp2660 charging algorithm.