I have used it for sealing wood but not too patch holes. It likely would work if the screws were left in then put the stuff over them. I wouldn't leave the screws in and the hole left may be too big for the flex to fill in.
Heat up a butter knife or tea spoon until it's hot enough to melt the plastic. Start just above the hole and with a slight weaving motion smooth the melted plastic over the opening. For added security, go back over in the opposite direction and then do the same to other side as well. Best to do this outside or in the garage if the spouse is around. Test your work before putting it in service.
...I'm starting to I think I've been a welder for too long.
Looks like polyethylene. Nothing wants to stick to it permanently, you need to find a product made specifically for that type of plastic. I have used 3M DP8005 successfully on a number of occasions but there may be newer options now. As a previous poster said a welded repair would also be effective but that material may not be thick enough for that.