Absolutely yes. In fact...been there, done that. Long story short, years ago we wanted to find a local babysitter there so that DW and I could enjoy a night or two in WDW on our own. Our kids were fairly young then, if I recall they were about 8, 5, 5 I think. We stay offsite, so we wanted a sitter to come to our rental house. We had used live in au pairs for years, so we were pretty familiar with interviewing childcare providers sight unseen (the au pairs are from other countries). I don't recall 100%, but we used sites like Care.com and Sittercity (or something like that). We interviewed several people via phone and decided on one. Turns out she is not only a local resident, she was a CM. The first time, she watched them in our rental home. It went great, the kids LOVED her. So after that, we asked her privately (so the kids wouldn't hear if she declined) if she'd be willing to spend a few hours in the park with them instead of just being confined to our rental home. She was all for it, and the kids were super excited. Ever since then, she has now become a family friend, and even at ages 13, 10, 10 the kids look forward to seeing her every trip. When we're putting together our loose outline for a trip, they always ask when they'll get to see her. They love exploring the parks with her, and we enjoy the "mom and dad" time. We even take her out to dinner sometimes, which is nice, so that DW and I get to spend some time shooting the breeze with her (when she babysits the kids just want to go running off with her, so we don't get to talk to her much, LOL.
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EDIT: In fact, to circle back to OP question about shopping, it's kind of funny...our kids always save part of their allowance/chore money in a special WDW envelope that they bring down with them for souvenirs. So it's not DW and I doing the shopping, it's the kids, and they want to do the shopping with her. We don't object, and yes, we often will use that time to do any gift shopping for the kids we want to do.
So I'd suggest using due caution and due diligence, but I would have no problem whatsoever with it. It's been absolutely wonderful for us.