Electrical tape won't save you.
No. Indoor extension cords are not built to handle moisture, temperature swings, or UV exposure. Wrapping the connection in electrical tape does nothing to seal the cord itself — water will find its way in through cracks in the insulation, at the plug, or along the length of the wire. Once moisture hits the copper, you’re asking for a short, a shock, or a fire.
The tape will also degrade quickly outdoors. Heat, cold, and sun turn it into a sticky mess within weeks. Even if you think you’ve sealed it perfectly, you haven’t. The National Electrical Code exists for a reason.
Buy a cord rated for outdoor use. It costs maybe $10 more and lasts years. This is not where you save five bucks.