No, because the grass seed needs light to grow.

Love to a see a photograph - why does it look awful? How did you lay it, that is, what's underneath, or have you just chosen one you don't like the look of?
No, you can't put down grass seed and cover it with the artificial turf. You can wait, then prepare and seed the area in March/April provided the ground isn't waterlogged or frozen, but bear in mind you will not be able to use it normally for at least six months, until its all grown and bedded in properly. Turf would be the quickest solution, but as its so cold currently, I'd wait till March even to do that, and again, ground preparation is necessary.

That would be a disaster

Maybe best to wait until the weather warms up and dries it. The football grounds covered with artificial turf seem to be ok.

Even artficially turf needs to be maintained. Seamless is a challenge, keeping down the ends and repairs not looking patchy, curled edges

I was on a coach trip and saw two football teams having a game on an artificial pitch in London. Amazed at the pounding that 'turf' was taking from 45 boots !

It always looks great when it's brand new

There's one opposite where I live Diane - its been there 8 years, and looks as good now as it did when first laid. But the trick with artificial turf is proper preparation beneath, the material you lay underneath it (preferably granite dust), infill material, and how its fixed down, otherwise it can look like a badly laid, cheap carpet...

It's often used for children's playgounds & miniature golf courses. For that it's ok.

Diane you've got me worried - did one of the players have three legs or have I missed something, lol?
Or did the poor ref only have one...