We've run very tiny quantum programs already, such as factoring 15 into 3 and 5, but it's been difficult to scale this upwards and work on larger numbers of bits at a time.
So, possible? Yes, for sure. Practical.... Not quite yet, maybe never, maybe soon.
And nobody I know really cares about bohmian mechanics. Only outsiders seem to since it seems edgy. I have some philosophical objections to it as well.
And as for Bohmian Mechanics, I think this is just a re-interpretation of quantum physics, and not actually a competing theory.
Trying to build computers in this case and diagnosing the errors then are likely to give us the data necessary for the discovery of the new, better theory.
Now, if it is possible in principle but not practical to engineer - that's what we need a golden age of engineering research to find out.