Speaking as someone who has a last name that, properly formed, would be "Ælwyn", and who happens to have a day job for a software company that writes, among other things, stuff for tracking "Land and Vital Records" ("Vital" being birth and death certificates, along with name changes)… in most places the kid would have problems, although there is pending and/or recent legislation (I can't recall which, offhand) that would require systems to cope with such names more effectively.
But in practice even then a lot of systems will transliterate it as a simple "AE" because most things treat it as a ligature rather than a distinct character, and decomposing a ligature is a typographical (presentation) change rather than a change of content.
But I wouldn't expect them to be appreciably more (or less) easily targeted by Unicode manipulations, really. Or at least if they are… it is going to be so far behind all the other headaches from systems that can't cope with them that they're not going to notice.
Yes, having three non-familiar names will also cause at least some systems to struggle with it, though probably far fewer — several systems at least allow for multiple "middle" names. Before changing mine (yes, the Æ is self-inflicted, and yes, I knew it wouldn't translate well, which is why legally it is "Ae") I had two middle names, or a single middle name and a hyphenated last name, depending on which way you interpreted it, and several times it did cause "interesting" situations — but hyphenates are at least fairly well supported almost everywhere in the US now.
To address the entirely valid point raised about Æ not strictly being a ligature: partially (or even mostly) correct. The character "ash" is not a ligature at all, and is in fact the proper form for words deriving from languages which used it (including my own last name). As for lexical vs. typographical ligature, all I can say is that even the Unicode standard can't seen to decide if it should be or not (see https://stackoverflow.com/questions/9376621/folding-normalizing-ligatures-e-g-%C3%86-to-ae-using-corefoundation for some discussion of this), but my actual point stands: in practice, a large amount of record-keeping software, if it can deal with it at all, will be prone to decomposing it (especially if anything like OCR software comes into play). To make it even more fun, unlike ẞ or the "Turkish I", there is a complete round-trip mapping between Æ←→æ.
0x04 EoTand it just keeps screwing me over. I'm glad to see I'm not the only one, but I do feel sorry for your cousin.