Yes it matters. Many of the cheapo cables and cables intended for light duty use like printers or monitors are most commonly only rated at 10A but some can be rated as low as 5A or 7A. For a psu, they should be ones rated at 15A.
What many fail to remember is that psus have an efficiency curve. If you have a 550w draw on a 80+ psu, that's actually closer to 700w pulled from the wall, about 6A. A 10A rated wire is going to get/stay warm and it's prongs can degrade over time and use, if it's actually UL rated and not just fake stamped . A 5A or 7A wire is in serious trouble.
And that's just the cable. The El-cheapo cables will also cut corners on the socket pegs itself, using sub-grade brass that doesn't hold tension on the pins, resulting in arcing and finally, fire.
If you buy a reputable brand like Corsair or Seasonic etc, they already know all this, and more besides, so it's better to always use the cable that came with that psu as they won't skimp on specs.
But if forced to use another cable, check the specs, it should be 15A rated, and therefore psu quality.
Those cables also come in different lengths, I've seen 1' extensions using 18ga with a 10A rating, and 6' cords with 18ga and a 10A rating. Not sure I'd trust the latter, that's a long cord and good amount of resistance per foot with 18ga wire. 16ga would be better. Some cords are as long as 25' but generally use 14ga wire and are 15A rated.