Only if you think the power dynamics between the two parties are equal. Or in other words, only if you think that both parties would get the same benefit (or harm) from some sort of mediated negotiation (e.g. both parties share their best offer with a third party who then follows some agreed-upon rule to settle the transaction at some price in the range of mutually-acceptable prices if any exist).
What you're describing (both sides providing a best offer) obviously doesn't work without some sort of agreed-upon method for sharing the offers before knowing the other party's offer and then settling on a price if any mutually-acceptable prices exist.
In reality, even an auction among a large set of workers and employers is unlikely to be have "ideal" outcomes (according to some reasonable definitions, although all definitions would be debatable), particularly when relevant qualities of the two parties are different (like how much information about the market each party has, how risk-averse each party is, etc.).