Oh yeah, absolutely. If Blood Angels Successor players get Mephiston and Death Company (under different names) I don't see why Ultramarines successors shouldn't be able to use 'Ultramarines specific' units or characters. I'm a firm believer the the point is 'list A' fights 'list B' through the medium of models, which are
all proxies anyway (ie, they stand for imaginary soldiers). The colour of those models doesn't alter the legality of the list (you could field Blood Angels in lime green or Dark Angels in pink, as long as the
list is legal - likewise, you could have Ultramarines in black or yellow or red and call them the Knights Who Say Ni, as long as the list is legal).
Don't agree that the Ultramarines don't have traits though. Their trait (or is it more like a doctrine?) is 'Follow the Teachings of the Codex' (listed in the centre, yeah?) which, uniquely, allows them to take all units from the main Codex, with no disadvantage.
Also not
quite sure (in fact, I'm afraid I know you're wrong) that all Ultramarines units are in the Codex (Astartes). The Tyrannic War Veterans were formed after the Conclave of Hera, in the teeth of traditionalists who argued that such a unit was contrary to the teachings of the Codex, in order to provide veteran units to fight the tyrannids.
On the Apoc rules, I don't have them either, but Son of Horus is generally pretty spot on about this sort of stuff.
And yes, I play Ultramarines too.