Does a routine alarm waste battery life?

This may be a silly question but I have my alarm set for 4 days a week on every week. So I am always seeing the small clock icon in the top bar to tell me that the alarm is set. There is no time that I do not have an alarm set to go off, even if it is for 2 days from now.

Does the fact that it is always "on" consume more battery life? Someone told it does, as having the alarm armed makes the clock constantly check if it needs to sound the alarm. This didn't seem very effficient to me. Or is it using just as much as the clock uses, to keep track of the time even when the iPad is shut down?

Of course I get that when the alarm actually sounds and has to play a tune etc. it would use battery but what about the time in between?

That is nothing to fret over. The software uses so little extra energy that it is not worth counting. Your OS is always doing something in the background anyway. Also, checking system time doesn't requiring using WIFI or bluetooth or GPS or lighting up the screen. Those things use way more energy than polling the clock in the background.