If you mean would a mini Strap You interfere with the bag handle on a regular (medium) size classic Peekaboo (and not an Essentially or an X-Lite, of which I have no experience), the answer is, yes, it will. I bought a mini strap and somewhat regretted it as it is uncomfortable and awkward on the shoulder, too close to the bag handle, and also isn’t great to carry it by hand either, because it sits very close in height to the bag handle. I do use it (I have one of the metallic studded ones) but view it as decoration, not a functional item.
I think I am right in saying that the regular size Strap Yous are all shorter and wider than the shoulder strap that the regular Peekaboo comes with. They would certainly work better as a shoulder strap with the regular/medium classic Peekaboo. I have one of those straps and that works fine. Most if not all of the Strap Yous are not adjustable, as far as I can remember, so you’d have to check they’re short enough for you. I’m not 100% certain whether all regular Strap Yous are the same length as mine, and I’m not at home right now and so I can’t double check, I’m afraid; however you should be able to see that on the Fendi site. So if we’re talking about a regular (medium) size Peekaboo, a regular Strap You might be what you need.
If it’s a mini Peekaboo you have ... I do have a mini Peekaboo but haven’t tried the mini Strap You on it and, again, I’m afraid I’m not at home right now so can’t check if the smaller bag handle and the mini Strap You would interfere with each other in the same way if it is to be used as a shoulder strap. Probably not, or I guess they wouldn’t sell them as ‘shoulder straps’ (though that just could be a translation issue ... ), but you might want to keep asking in case someone else can answer on that point. However the mini straps are undoubtedly quite short and you would be using your mini Peekaboo tucked quite high under your arm, I THINK, from memory and extrapolation, almost small Baguette-style.