Keep in mind that your growing a tree. They are going to get big. If you look at people that build mangrove refugiums, they tend to be in a large tank on the floor, so the mangroves can grow tall.
There is nothing to prevent you from putting some in the display tank, but as they grow they will block more and more light and you'll need to raise your lighting up to accommodate them. On the other hand, if you want mangroves and few corals, a mangrove biotype could be very interesting.
I wouldn't expect the mangroves to take the place of a sump, unless your planning a "forrest" of them.
The bottom line is this all depends on what you want to keep in the system. No really right or wrong answer here.
