I’ve grown them through weed membrane and it is fine, but I would really water the soil well before you lay it. It does allow a few more weeds through, but make a decent hole in it to plant through. That makes watering and feeding the plant a lot easier.
You do have to look out for slugs lurking under it so I would sprinkle some slug pellets around as a precaution even through it has gone hotter and drier.