"7805 data sheets do not specify any minimal voltage input . "

You will have to recheck on that statement. In any case for a 7805 the safe input value will be 5+3 = 8 Volt generally. This is just a handy thumbrule and the best bet is the data sheet value.

"When I powered the micro and the peripheral directly without the regulator they work just fine "

Depending on the load to drop the supply to safe levels is bad design. So no point finding out whether it is OK or not. With very low voltage you can have a hung MCU and on the other end with high voltages you can have a cooked MCU. Somewhere in between things MAY work.

"The power consumption by putting an ammeter in series works out to ~100 mA idle mode and 270 mA while scanning."

Appears to be way too high for a handheld device. But since you say it is only for a second , have you thought of SuperCaps ? There was a discussion on this forum recently. Search.

Raghu