Yes.
Chickens that were properly vaccinated with Marek's Vaccine, if exposed to the virus at ANY point in their lives, will contract the virus.
Chickens that have built resistance (via the help of the Vaccine) will not show symptoms, but the virus will live in latency in their cells, and they have the potential to spread it.
Chickens that have not built resistance (either because the virus challenged the immune system and won, or the vaccine was not given properly, or the chick was not given enough time to build resistance, etc), even with the vaccine, will become symptomatic and may die, or recover. It is hard to say.
There are a lot of variables. If you want to do some more in-depth reading about the vaccine, you can go here:
https://www.backyardchickens.com/a/the-great-big-giant-mareks-disease-faq
In short: Yes, ANY chicken that is exposed to Marek's virus and inhales it will actually contract the disease, vaccinated or not. It's just that vaccinated birds have a higher chance (anywhere from 50% to 90% chance depending on the virus strain) to build up resistance and those that do never actually get "sick". The virus will still live in these birds, without harming them.