Teflon (plumbers tape) to seal hot water pipe leak from the outside?
No.  "Teflon tape" is used on the threads of joints, not to seal leaks outside of joints.  It's not adhesive like tape, so it wouldn't stick to the outside of the pipe at all.

If you don't know what you're doing, I'd bring in someone who does.  Based on the amount of corrosion, it looks like it's been leaking for some time. It could be as simple as tightening the nut, or it might require disassembly and reassembly (possibly with new parts).