The timing that actually matters for a cash purchase is ordinary: coordinating condition removal, a home inspection typically running $400 to $600, and the lawyer who moves title through Information Services Corporation on possession day. None of that shifts because of a rumoured tax elsewhere.
Cash does simplify the closing itself, since there is no lender, no CMHC or Sagen insurance premium and no mortgage approval condition to satisfy, which is usually why a cash closing feels faster than a financed one.
Close on the timeline that works for the condition, the lawyer and the seller, not around a tax that has no basis here. Get your hand-reviewed valuation from Joel Dyck.