Reaction between CH3CH2Li and Ethyne
Terminal alkynes are weak acids, but they are still stronger ones than alkenes and alkanes. This actually means they would readily react with conjugate bases of weaker acids, giving them the proton. So yes, since ethyne is a stronger acid than ethane (and ethyl anion is a stronger base than ethynyl anion - the list for bases is reverse due to obvious reasons), they will exchange H and Li.

Below you can see a mechanism I would use to describe the problem in your question. C-Li bond has significant contribution of both covalent and ionic components, so I wrote it as both in equilibrium: