Most people can hang upside-down without puking. The human digestive tract is lined with muscles that keep everything in place and moving in the right direction. If you can physically keep from puking at -1G (by your frame of reference) then you can certainly keep your lunch down in 0G.
Going beyond your question though, space sickness happens because the bones and fluid in your inner ear that determine your orientation float around. You can have the ceiling as your frame of reference as “up” and then a small shift causes your inner ear to register it as down, left up, behind. You get nauseated from that and you puke.
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