A few years ago I had to ride a 10 mile or so TT in sneakers because I forgot to take my cycling shoes.

I ended up taking off the TT bars because I couldn't ride the bike with them and not having shoes clipped in. It was too unstable that way.

So I rode Merckx style in sneakers without toe clips.

It sucked, but it wasn't that much slower than I would have expected otherwise.