In my experience, they always check the contents on International flights departing from the States but I have yet to have it happen on flights entering (unless by US customs). Most of the time this is just Xray machines but I have had them ask permission to open items about 20% of the time but they have always been really helpful repacking them. I mean I was standing there once pulling my underwear and tons of crap from around my bicycle frame but I think they have seen it all so no worries.

Why would this matter though in regards to your packing? I seem to remember them having tape and stuff there for your usage. Otherwise just bring a roll of tape and some zip ties and give yourself some time to do it all.