I will preface that this is the US and I can't speak for anywhere else since systems could be different.
Story time: I once heard another customer chatting with her SA at the register next to the one I was at (checking out with my SA). The SA was saying how she could see this client buying stuff online from time to time, and just very recently a herbag. But when she looked closer, it has an address on the opposite coast of the country. So she realized it's someone with the exact same name as her client! SA joked how this made her feel better because she thought for a moment the client was "cheating" on her (jokingly so I didn't find it offensive but I think it's a word that some may find problem with).
I think if your SA searches their database on customer history, they can search by name (mine has done it too). In this case, when the SA searches for her client using the name, the other person with all the web purchase history comes up. So if your SA searches with your name, for sure she can find this purchase.
And I do think - depending on the SA - they may feel not so good about it. The way I do it is if I see anything available online I want I immediately tell me SA. She can click to order, ask for transfer, etc. for me and I hope it still gets her commission. As a matter of fact, I asked her (after overhearing that conversation I recounted above) if I can order stuff online with her and she replied yes, that's exactly why I've been doing it this way. Of course, the problem is that if it's a super covetable item that will disappear immediately you can't wait and have to get it as soon as you can. My SA is personally cool with that - in the same conversation she also said while I can always come to the store to order H.com stuff with her, if it's something that will be gone in a blink, unless I live right above the H store (I don't, lol) then the only way is to just grab it online.
Wow turned out to be a long post! In conclusion, I think your SA will definitely see your purchase but she may not mind if it's a very hard to get piece. Talk to her is a good idea but I don't think you need to go out of your way to say sorry or act like you did something wrong, just mention it to her the next time you go in!
And good luck on your wishlist bag

hope it comes your way soon!