I like grocery shopping (and pretty much everything about cooking), so I wouldn't do it myself.
I would also wonder if I'd missed the better deals: Comparing the cost of pre-chopped peppers to the 3-pack of whole peppers. Picking up the unplanned items from the clearance area (for example, I currently have TEN corned beef briskets in my freezer -- they averaged $4 each; no, they weren't on my list, but when I saw the price, I filled my cart). Noticing that pork chops are on sale; thus, I'd better add the items I need for my husband's favorite pork chop casserole. Thinking about it this way, I suspect it would cost me more than the published $120/year.
However, I have a friend who has two small children, and she uses an order-online-drive-up-and-get-it service. She says it's totally worth the money because she doesn't have to get the kids out of the cars /into the buggy /say no 1000 times to cookies and sugary cereal /get the kids into the car ... you get the idea.
And it would be nice at certain times in your life. For example, my mother had some major surgery recently -- having food delivered might've been worth the cost during her recovery. And my grandmother stopped driving in her elderly years -- again, a delivery might've been worthwhile for her, if she hadn't had family to take care of her needs.