Good question. So yes this can be done. Say that you do repeated SVD's of a tensor in the way that you described, then manually set the tensors of an MPS using the results of these SVD's. Then you are right that the orthogonality center will not be defined for this MPS object, even though the tensors are known to you to have the orthogonality property.
So to fix this, after you finish setting the MPS tensors, you can call the .leftLim(ll) and .righLim(rl) methods on the MPS. Here ll and rl are integers saying what value you want the leftLim and rightLim to have.
(More documentation here: http://itensor.org/docs.cgi?page=classes/mps
For the specific case of site 1 being the orthogonality center, if the MPS is called "psi" you should do:
Likewise, if you want the center to be "j", you should do .leftLim(j-1) and .rightLim(j+1).
As I write this, it occurs to me that it would probably be good to have a convenience function that just takes the center site number "j" and sets the left/right lim for you.