That's fantastic (re: iFixit sending you a cable) -- that is hands down the proper fix for this.
So to answer your original question: no, I would not recommend soldering the antenna back together. The reason has to do with the kind of solder used combined with the leftover flux; meaning, a soldered-together antenna wire I would expect to perform abysmally compared to a non-soldered-together antenna.
It's a different situation when you get into larger antennas (like the ones on rooftops), where you can quite literally weld (or alternately melt down and merge) the pieces back together with little repercussion (AFAIK).
Opinionated footnote: I hate these damn antennas used in portable devices (mobile phones, laptops, etc.). They're just such utter crap
. Like the absolute cheapest garbage they can find, yet people wonder why they have problems connecting to wireless devices 10 feet away. These places would use braided rope if it worked! The focus is entirely on thickness/size/blah blah, when in fact this just really doesn't cut it when it comes to an antenna. You really have to have something good/well-made when it comes to that.--
Making life hard for others since 1977.
I speak for myself and not my employer/affiliates of my employer.