All armies and fleets destroyed - Still in Game?
The quote below is part of a rule.
So yes, I would play it like you suggest, because your situation matches this rule in the strictest sense (one center versus zero units).


  If he/she has more centers than units, he/she may build units by placing them, one in each unoccupied supply center, in his/her home country only (provided that such supply centers are still under his control).