I don't work at Safeway,(I work in another big supermarket) but, I think it highly likely she could shop there.
Why ever not? She needs her food too and I would think no-one would reconize her particularly.
Wev'e had the odd tv personality go thru ours (I've been told) and I served Jane Torvill once myself (1984 world Ice Dancing Champ) and she went thru with no hassle from anyone.
She and her ice partner are like a national treasure here and she just sailed thru totally un noticed.I'm sure it would be the same at Safeways.