In theory, yes. The thin winding wire will be insulated, so you'll want to try and scrape the insulation off before soldering (fine sandpaper or a Scotchbrite pad). Some insulation material will burn off with heat, but if you can remove it first, then it's better.
I'd solder a thin piece of solid wire in the white wire eyelet first, then run it parallel to the broken wire and solder those together.
Don't try and stretch it so it reaches the eyelet as it will break again, and then it will need a rewind.
I take it it is a 'proper' Fender pickup with magnetic pole pieces, rather than one with magnets stuck underneath as found on some Mexican or Japanese Fenders? If a proper one, it's worth getting it rewound if you can't fix it yourself. But not worth it if it's one with magnets on the bottom.
Last edited by Simon Barden; 03-02-2022 at 04:27 PM.