Duct boosting fans are not to be used with carbon filters because they are for just moving air down a duct that already has a proper inline fan attached. They do not handle resistance. Seen a lot of folks fail trying to use them.
But it might work with just a filter and zero bends or duct.
A proper extractor fan can lose 10% per bend, 20-30% for a filter and 5% per meter of ducting. Although there are many "proper" extractor fans and results depend on the impeller type. A box fan can shift a huge amount of air for low wattage but put more than a few meters of duct and a filter on it and its down to 40-50% airflow. A centrafugal fan can shift a bit less air overall but some only lose 20-30% on huge lenths of duct and many bends. They have different pressure ratings. Operate differently.
There are lots of cheap fans that work these days. Hundreds of second hand ones too.