If a Japanese person calls you older brother/sister(お兄さん, お姉さん), in addition to implying closeness, does it also mean that they are implying a platonic relationship?
By "older brother", I assume you mean お兄さん.
By "older sister, I assume you mean お姉さん.
If so, then this is one type of way of referring to men/boys and women/girls who are not so old as to merit おじさん おじいさん おばさん おばあさん.
I was a bit surprised at this mode of reference the first time someone did it to me, but it's pretty common.
It does not necessarily imply anything at all about closeness. First person to call me お兄さん that I an remember was a plumber working on my apartment. I hope his intentions were platonic, but I don't know if using this marks off one's intentions in that way.
If you mean putting 兄 or 弟 after someone's name, then I've only seen that in churches. (there may be other contexts).