So I have no background in Advertising per se, but my brother is an executive at an agency, wife works for one, and have a lot of friends in the industry. While in b-school, I gave a lot of network contacts to some classmates so can give you some insight into transitioning via an MBA. The switch completely depends on what you think you want to do in advertising. Want to be a creative and go become a copy writer after school, sorry not going to happen. Strategy planning on the client side will be more doable but also a stretch without the background. Accounts, probably not an area you would want to go into. Corporate type support roles such as strategy, finance, HR, etc probably the easiest path in with an MBA but not as focused on the clients so may not be what you are looking for.
Pay in advertising is like banking on a smaller level. Undergrads get paid slave wages and can't even get by in NY, they hire a lot and burn out tons of people. If you advance quickly and don't exit the industry you can reach a high level where the pay is extremely good if you are a top performer. Job security can be iffy for some people, lose a big account and your job may follow. Make it to the executive level and you will make a pretty substantial income and have a lot of input doing what many people think is a really cool job. The cultures vary greatly but tend to be very liberal, you can have neck tattoos and a mohawk, and it wont hurt your career depending on your company and function.
The sticking point for most people is the salary range and entry point is not as attractive as many other post-MBA paths. Most agencies are not huge operations, it is like consulting in a way where you have some huge ones but then a lot of smaller niche agencies. However, tons of agencies are owned by large advertising holding companies (Omnicom, WPP, Interpublic and Publicis). I wouldn't try to talk you out of it, because I know how successful some people can be and the life that can lead to. Hours can be really demanding and travel can be extensive depending on the job. Security is not always that great, but if you build up a good network and reputation finding a landing spot isn't that challenging.
I would reach out to your network and find some people who work in it or used to. Pick their brains, don't be afraid to find Kellogg alums at agencies and reach out and ask them if they think it would be a smart move. Leo Burnett is right downtown and there are a fair number of alums there, use Linkedin and just ask. People who aren't in the typical MBA career paths tend to love to talk about it more than people at MBB, just because they aren't bothered about it a lot and if they are passionate about what they do they will want to share.
Kellogg Class of 2010...still active and willing to help. However, I do not do profile reviews, don't offer predictions on chances and am far to busy to review essays, so save the energy of writing me a PM seeking help for these. If I don't respond to a PM that is not one of the previously mentioned trash can destined messages, please don't take it personally I get so many messages I have a hard to responding to most. The more interesting, compelling, or humorous you message the more likely I am to respond.