Agree with the comments above. No way those will hold the rail loaded with curtains for any length of time in drywall (I repair this kind of failure ALL the time, as rarely do things ship with suitable fasteners...).
You need a fastener which opens out on the backside of the drywall but it depends on the construction of the house. Whats behind the drywall? Timber frame or masonry?
I see you're in the UK, so it's likely the drywall is stuck to blockwork using an adhesive (dot and dab). In that case the second fixings would be better as it would get into the wall itself.
Drywall doesn't have good holding power unless you can get behind it using a fastener which opens out (not possible on 'dot and dab') or through it and into the wall.
NOTE: Where you have drywall bonded to masonry, use a 7mm or brown rawlplug and drill a hole deep enough to ensure the whole of the brown plug is in the masonry.
Typically this means a 8g or preferably a 10g screw at least 65mm or 2 /12" long.