Can a plastic fridge shelf be definitively repaired?
There is no glue job that involves just the edges of the plastic shelf that will hold up to any use. In fact it is rather amazing that you got it to bond with PVC pipe cement. Clearly the solvent in the pipe cement that you used was able to temporarily melt the plastic edges to the point of them bonding back together. 

In order to get the fix to stand up to regular usage you are going to have to do some additional work. Find a type of glue that really takes to this type of plastic and use that to bond some metal cross bars to the bottom side of the shelf surface. Something like aluminum bar stock that is 1.5" (~38mm) wide by 0.25" (~6 to 7mm) thick that spans the maximal across the width of the shelf would be workable. I would suggest three such bars. 

The ridges on the shelf, which appear to be on the bottom side, will require you to use a bonding agent that can fill in a gap. I would not recommend grinding off those ridges to accommodate the suggested cross bars. I would also not suggest trying to drill holes and using fasteners to secure the bars. This creates localized pressure points in the plastic that could cause it to crack from the drilled holes. 

Experiment with silicon sealer type material to see of it bonds to that type of plastic. The plastic has to be clean, dry and oil free. If it does this would work well to bond the support bars to the bottom of the shelf. Silicon sealer material bonds very well to aluminum bar stock. If the silicon sealer is a non-starter with your plastic shelf then you could try one of the construction type adhesives. There are types that have solvents that allow them to bond well to certain types of plastic.