Should I accept the request? This might help the person to understand
that I am now aware.
Yes, you should accept the request.
The whole point of people sending you this "meeting request" is to put it on your calendar. That way, whenever you look, you'll see that they are out.
This is becoming a reasonably common practice in many shops, including mine. With small teams, it seems to work well.
The problem is that people will look at my calendar and think I am
It won't mark you as busy if the sender sets it up correctly.
Depending on the mail/calendar system you use, the sender can set it up to indicate the time is "Free". On some systems that could be used to mark their absence on your calendar without marking you as "Busy". See: https://support.office.com/en-ca/article/Keep-everyone-informed-about-time-away-from-the-office-69fe38aa-7b5f-4225-8b69-47f47092e65e?ui=en-US&rs=en-CA&ad=CA
Try it - you might find it's a handy way to keep track of who is around and who is not. If you find after a while that it is cumbersome, or doesn't meet the needs of everyone, you could suggest another method.