Today I contacted a deacon from my church who really knows this stuff. He knows Syriac, tutors students in it, and he did a masters thesis on St. Ephrem the Syrian. He is currently working on a translation of some of St. Isaac's works into Modern Armenian.
First off, he said we shouldn't call St. Isaac "Soorp Sahag," but rather "Soorp Eesahag." He said people who call him Sahag are "Armenizing" his name. So properly his name would be Soorp Eesahag Ninvetsi, or Soorp Eesahag Asoree.
He confirmed that the ethnic divisions we see now were not really there at that time, which is why Asoree could be translated as Syrian.
He said that although St. Isaac is not on our calendar, he wrote nothing that was objectionable to our theology and some (not all) of his works were translated into Classical Armenian in the middle ages. So he may not officially be a saint, but at the very least you can say his works are respected by the Church.