I'll say yes, but I need to qualify that 'yes'. I have direct sowed into the gritty mix your asking about several times with no problems at all. I usually arrange the seeds on top & cover them with a thin layer of sand or fine Turface from the screenings of the Turface that goes into the soil. I mist lightly, keeping the soil damp, but not wet.
I've also started LOTS of cuttings in the gritty mix and have a very high strike rate.
That said, and if I'm honest, I have to say that while the Turface and granite component would be considered sterile, the bark component wouldn't; so you can respect the possibility that it could bring problems, or just move forward and see. Personally, I wouldn't worry about it unless the seeds were something very special (to me). If they were, I would use screened Turface or screened perlite - situate the seeds on top, and cover with a thin layer of sand or fines left from screening the Turface.
The disease you need to watch out for is 'damping off', and it's caused by any one of several species of fungi. Wet conditions and lack of sufficient air movement is key in these fungi growing to sufficiently high populations that they cause problems. Since it's very difficult to keep the top layer of soil wet (but not damp) when using the gritty mix, the biggest concern should be providing good air movement, which you should try to provide no matter what media chosen.