Yes, I think that many anthropology experts aspire to be like Indiana Jones, because he made it look exciting to be an anthropology, and even a little bit sexy. There is nothing wrong with wanting to be like him. Jones took a field that might appear boring to some people and make it look interesting. Good for him.
Indiana Jones is actually seen as big part of the archaeological image in the US, and Harrison Ford has even been made president of the American Archaeological association. Still Jones' methods in the movies are absurd, and should never be replicated by professionals, even if the image has been beneficial to the trade.
Indiana Jones is a fictional character and everyone recognizes that he is not real. Although his movies are popular, no one actually aspires to be like him. Real anthropologists are serious academics, and they do not want to live their lives like a Hollywood movie. Movies are just an escapist fantasy.
Not really. I'm sure that Indiana Jones might have inspired more than a few people into careers working with ancient cultures (and by the way, he was an archaeologist, not an anthropologist). However, anyone who has been in the field for more than a few years knows the reality of the profession.
To become an anthropologist, students would typically not only have to go through a four-year college, but also seek an advanced degree (PhD). It's doubtful after that much schooling and experience that they would still believe they were going to spend their lives having fun and going on amazing adventures. Reality would hit them long before that. That being said, many might aspire to make exciting new discoveries and learn more about humanity, and that would likely be a reason to want to become an anthropologist.