This is one of those extreme questions where the answer is "yes, everything evaporates" and "no, you shouldn't act as though everything is evaporating."
In chemistry class, we typically talk about reversable and irreversable chemical equations. Reversable ones achieve some equillibrium concentrations, while irreversable ones end up with all of one compound or another. It's short, succinct, and wrong. But it's good enough to be really effective in virtually all cases!
In reality, all chemical transformations we find are reversible, existing in some equilibrium or seeking an equilibrium. So yes, there is an equilibrium concentration of metal atoms in a solid with metal atoms in gassious form.
However, that equilibrium can be so lop-sided that we can't even measure it. When this happens, we call it irreversable because there's really no reason to think otherwise.
In the theoretical side of things, this is known as entropy increasing. The entropy of a gas is higher than that of a solid, so there is a very slow shift towards things evaporating. If you start talking on timescales of 100,000,000,000,000 years, this effect is very powerful. In fact, wait long enough and we have reason to believe protons, themselves, may evaporate! However, on human timescales, it's not so useful. Practically speaking the rate that metals evaporate into the air is so extraordinarily slow that we can basically ignore it.
The most famous example of this thinking that I know of is from the high vacuum physics world. High vacuums are the really nasty vacuums that make the vacuum of space look weak and tepid. In that world, there's a phrase, "everything outgasses." Everything you put in a high vacuum chamber evaporates. Many things that we think of as a solid or a liquid evaporate/sublimate fast enough to actually mess with your vacuum. At these extreme vacuums, there aren't very many atoms bouncing around in the first place, so just a little evaporation makes a big deal. A single fingerprint can outgas for weeks, preventing you from pulling the high vacuum you seek. Thus those who work with vacuum chambers are very strict about cleaning surfaces to remove such artifacts.
Of course, some things just don't have a smell. In high vacuums, we see lots of hardware made of stainless steel. The chemical bonds in stainless steel are very strong so it evaporates very slowly. It evaporates slow enough that we can't really detect it, so we treat it as though it doesn't evaporate.