Yes; the person who invites you to dinner is expected to pay for the bill, and the tip. Such an invitation would be worded something like, "I'm taking out all my friends to dinner next week for my birthday," or "I'd like to invite you to Fratelli's for spaghetti."
However, that is different than someone who is simply acting as an organizer. As long as the organizer informs you up front as to what is expected, you are free to accept or decline, as you wish:
"Hi, this is Becky. Some of us are getting together at 7:00 Thursday evening, for dinner and drinks at El Chico on Maple St., for Sandy's birthday. We're each going to pay our own way, and we're each going to chip in $5-10 to pay for Sandy's meal and drinks, and some people are going to bring gifts, others aren't. Would you like to join us?"
You can say "Yes", or you can say "No", or you can say "I'm not sure; I'll be there if I can." The only thing you could wrong would be to show up and then refuse to chip in for Sandy's tab, or to say "Yes" and then not show up at all (that could screw up the reservation count).
Note: if the "organizer" does not make the arrangements clear, it is your responsibility to ASK.