Yes there is a boost in growth after you build a station. Any station, train or bus or tram. But what happens after the BAM ? Rate of growth is improved? Clearly not otherwise I wouldn’t have 2 cities in different conditions with same amount of inhabitants.
I think the cities in game is not suppose to grow too fast. They are limited to grow slow to not take over the entire map. And some new constructions and upgrades happen after you make a station to make you feel you have an influence on that. But after the first BAM all you get is steady growth. All cities have a slow steady growth.