Not a materials scientist, but it's an interesting idea, if not valid. Most synthetic rope is made of nylon. I don't know how the plastic in bags compares, but bags do stretch and rip with only slight provocation. Considering the strand size in common rope, you might have trouble.

Then again, I have a backpack that's supposedly made from recycled plastic bottles, and it's held up for many years. Whatever it's made of, it's outlasted its leather trimmings.

Braid a four strand rope, stretch it as far as you can without breaking, and rebraid the stretched ropes into one (giving you 16 strand rope). I've done this every now and then with the bags the newspapers come in for years. They are quite strong, though I've never used one where the integrity of the rope might matter.

These days, plastic grocery bags are usually made of high density polyethylene (HDPE). Incidently, this is also what milk jugs are made of. Rope is not usually made of HDPE, although it probably can be. Rope is usually made of nylon, polypropylene, or polyester. Plastic soda bottles are made of a type of polyester (PETE) that is often recycled into fiber. It's mostly used for carpet fiber, but is also used for polyester rope. HDPE photodegrades faster than PETE and many grocery bags are specially formulated to degrade even faster than normal, so it might not make the best rope.