Yes you can. However, with some woods, the slight color variation between the filler and the real wood may become more apparent, while with others, oil finishes tend to even out things.
I don't know what will happen to bloodwood. Best to try on a piece of scrap first and see if you can live with the results. In this case I would not choose a penetrating oil, but go for a polymerized Tung oil finish, which is more a film-forming finish.
If you choose to stain before finishing (highly unlikely with bloodwood

), that always gives problems with this kind of wood filling. For that purpose they sell a wide variety of different colored sticks , made from a sort of hard wax, to be matched with the final results after staining, or even completely after finishing. That's another option you have, but it's more expensive and the results aren't always as good as with the dust+glue filler.
Bart.