Notification LED's generic power consumption
The power consumption isn't noticeable. Even a tiny watch battery can run a small LED for a few days continuously.

Increasing the blink rate won't change the power consumption at all: what makes a difference is how long the "on" part of the blink is compared to the "off" part. This is called the duty cycle of the LED.

Most LED controllers use the duty cycle to control the brightness of the LED (because LEDs aren't sensitive enough to voltage), so even when the LED appears to be on continuously, it's actually blinking faster than you can see. You can see this by waving the phone around in a darkened room: instead of tracing a continuous line in the air (like a sparkler or torch does), it looks like a dotted or dashed line. If you can keep the waving speed constant, and measure (or estimate) how long the dashes are compared to the gaps, you know the duty cycle.

The only reason for the LED to blink is a human one: to make it more eye-catching, so you can see when you have a message (or whatever).