Yes - it is included. Lasts between 1 and 1.5 years for me (I use the pen rather frequently). Experience based on 2 models (Pro 3 and Pro 4).

What can still be a bit annoying is that these batteries (AAAA) are not available everywhere (although this has improved in the meantime - the first time I had to "order" them specially, but now they are in stock at various places). Since then, I have always kept a spare copy at home, because it is annoying to have to do without the pen for several days.