Do we know at which angle the Event Horizon Telescope will look at the accretion disk of Sagittarius A*? Additionally, would it matter if we are exactly in the plane with the accretion disk, i.e. could we still observe the event horizon?
We don't know the answer to this (or if someone does, I'd really like to hear that answer). Our galaxy's Super-Massive Black Hole (SMBH) is an unusually quiet one, with little to no accretion disk. If one indeed exists, and it almost assuredly exists, even if it is tenuous and small, we have not yet seen it.
Around 2013, there was a gas cloud designated G2 that was expected to be accreted which would have given us a lot of insight into the black hole and its structure. Unfortunately there was little to no activity observed. A Nature article about this gas cloud goes into more detail and talks about the accretion disk, as quoted below.
The cautiously predicted flare-up would be a valuable probe of the environment immediately surrounding the black hole, about which little is known. What we do know is that the average rate of mass accretion driving the emission from Sgr A* is exceptionally small, thus explaining why our Galactic black hole is extremely dim. That we can detect it at all is due largely to its proximity — it is about 100 times closer to Earth than the nearest supermassive black hole in another galactic nucleus, that of the Andromeda galaxy. We also know that the accreting gas is heated so much that the individual gas particles almost all approach the speed of light, and that the observed emission emanates from a magnetohydrodynamic maelstrom. But the basic parameters of this small-accretion-rate regime are still being sought: does the accreting gas form a well-defined disk or an outflowing jet, as it often does in the more prominent cases observed in many other galaxies? Or is it better described as a more isotropic inflow comprising stochastically distributed density fluctuations?
After some research, I think this answers my question: The orientation of the disk seems not to be known with certainty, however, Meyer et al. (2007) gives estimates with $3\sigma$ confidence that "the position angle is ∼60◦−108◦ (east of north) in combination with a large inclination angle", meaning that the disk is seen more or less edge on.
This 2009 paper indicates that the orientation of the disk will of course influence the pictures, but in any case one will see the event horizon. I assume that this has to do with the strong gravitational lensing, basically projecting the plane onto the sky.